CLASS 11 PHYSICS • MOTION IN A STRAIGHT LINE

Acceleration and Retardation

Understand acceleration, retardation, rate of change of velocity and advanced motion concepts with NEET, JEE and CBSE level numericals.

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1. Acceleration

Acceleration is the rate of change of velocity with time. It is a vector quantity, so direction and sign matter. SI unit is m s-2. Positive acceleration means velocity is increasing in the chosen positive direction or changing toward positive direction.

a = Δv / Δt

Positive Case

Velocity changes toward positive direction.

Negative Case

Velocity changes toward negative direction.

Physical Meaning

Acceleration measures how quickly motion state changes.

2. Average Acceleration

Average acceleration is total change in velocity divided by total time interval. It can be positive, negative or zero.

Average Acceleration = Change in Velocity / Total Time

Positive Case

Velocity changes toward positive direction.

Negative Case

Velocity changes toward negative direction.

Physical Meaning

Acceleration measures how quickly motion state changes.

3. Instantaneous Acceleration

Instantaneous acceleration is acceleration at a particular instant. On a velocity-time graph, it is the slope at that instant. Calculus idea: it is the limiting value of Δv/Δt for a very small time interval.

a = slope of v-t graph

Positive Case

Velocity changes toward positive direction.

Negative Case

Velocity changes toward negative direction.

Physical Meaning

Acceleration measures how quickly motion state changes.

4. Negative Acceleration

Negative acceleration means acceleration is directed opposite to the chosen positive direction. It does not always mean the body is slowing down; if velocity is also negative, speed may increase.

a < 0 in chosen sign convention

Positive Case

Velocity changes toward positive direction.

Negative Case

Velocity changes toward negative direction.

Physical Meaning

Acceleration measures how quickly motion state changes.

5. Retardation

Retardation or deceleration is acceleration opposite to velocity, so speed decreases. Braking vehicles, upward motion under gravity and frictional slowing are common examples.

Retardation = magnitude of acceleration opposite to velocity

Positive Case

Velocity changes toward positive direction.

Negative Case

Velocity changes toward negative direction.

Physical Meaning

Acceleration measures how quickly motion state changes.

6. Physical Interpretation

Acceleration describes how velocity changes: constant acceleration gives straight line v-t graph, variable acceleration gives curved v-t graph, zero acceleration gives constant velocity.

Area under a-t graph = change in velocity

Positive Case

Velocity changes toward positive direction.

Negative Case

Velocity changes toward negative direction.

Physical Meaning

Acceleration measures how quickly motion state changes.

7. Graphical Understanding

Velocity-time graph slope gives acceleration. Acceleration-time graph area gives change in velocity. Position-time graph curvature indicates acceleration.

Positive Acceleration

v-t slope +

Negative Acceleration

v-t slope -

Zero Acceleration

v constant

8. Solved Numericals

CBSE Numerical

Question: Velocity changes from 5 m s-1 to 25 m s-1 in 4 s. Find acceleration.

Given: u=5, v=25, t=4 s

Formula: a=(v-u)/t

Calculation: (25-5)/4 = 5 m s-2

Final Answer: 5 m s-2

Exam Tip: Use change in velocity, not final velocity only.

NEET Numerical

Question: A car slows from 30 m s-1 to 10 m s-1 in 5 s. Find acceleration and retardation.

Given: u=30, v=10, t=5 s

Formula: a=(v-u)/t

Calculation: (10-30)/5 = -4 m s-2

Final Answer: acceleration = -4 m s-2, retardation = 4 m s-2

Exam Tip: Retardation is magnitude when speed decreases.

JEE Main Numerical

Question: From a v-t graph, velocity changes linearly from -10 to +20 m s-1 in 6 s. Find acceleration.

Given: u=-10, v=20, t=6

Formula: a=(v-u)/t

Calculation: (20-(-10))/6 = 5

Final Answer: 5 m s-2

Exam Tip: Signs matter in velocity.

JEE Advanced Numerical

Question: A particle has v = 3t2 + 2t. Find instantaneous acceleration at t=2 s.

Given: v=3t2+2t

Formula: a = rate of change of velocity = 6t + 2

Calculation: 6(2)+2 = 14

Final Answer: 14 m s-2

Exam Tip: Differentiate velocity for instantaneous acceleration.

IB Numerical

Question: Velocity changes from 12 m s-1 east to 4 m s-1 east in 4 s. Find acceleration.

Given: same direction, u=12, v=4

Formula: a=(v-u)/t

Calculation: (4-12)/4=-2

Final Answer: -2 m s-2

Exam Tip: Negative sign shows acceleration opposite chosen east direction.

IGCSE Numerical

Question: A cyclist starts from rest and reaches 8 m s-1 in 4 s. Find acceleration.

Given: u=0, v=8, t=4

Formula: a=(v-u)/t

Calculation: 8/4=2

Final Answer: 2 m s-2

Exam Tip: From rest means u=0.

A-Level Numerical

Question: Area under an a-t graph is 18 m s-1. Initial velocity is 5 m s-1. Find final velocity.

Given: Δv=18, u=5

Formula: v=u+Δv

Calculation: 5+18=23

Final Answer: 23 m s-1

Exam Tip: Area under a-t graph gives Δv.

Graph Numerical

Question: Slope of v-t graph is -3. Find acceleration and state motion meaning if velocity is positive.

Given: slope=-3

Formula: a=slope of v-t graph

Calculation: a=-3 m s-2

Final Answer: -3 m s-2, slowing down if v positive

Exam Tip: Negative acceleration can mean retardation only when opposite to velocity.

9. CBSE Theory Questions

1 Mark

Question: Define acceleration.

Answer: Rate of change of velocity with time.

2 Mark

Question: Differentiate negative acceleration and retardation.

Answer: Negative acceleration is acceleration in negative direction; retardation is acceleration opposite to velocity.

3 Mark

Question: Explain acceleration from v-t graph.

Answer: Slope of a velocity-time graph gives acceleration. Positive slope means positive acceleration, negative slope means negative acceleration.

5 Mark

Question: Explain average and instantaneous acceleration with examples.

Answer: Average acceleration is change in velocity over finite time; instantaneous acceleration is acceleration at a particular instant, found from slope of tangent to v-t graph.

10. NEET Question Bank: 50 MCQs

Authentic year is mentioned only when certain; otherwise cards are clearly marked exam-style to avoid fake PYQ years. Click a question to reveal answer.

NEET Exam-style Question 1: Acceleration is defined as
(a) rate of change of velocity(b) rate of change of distance(c) distance/time(d) velocity/time

Answer: rate of change of velocity

Solution: a = Δv/Δt.

Exam Tip: Remember acceleration involves velocity change.

NEET Exam-style Question 2: SI unit of acceleration is
(a) m s-2(b) m s-1(c) m(d) s

Answer: m s-2

Solution: Velocity unit divided by time gives m s-2.

Exam Tip: Check units from formula.

NEET Exam-style Question 3: Slope of velocity-time graph gives
(a) acceleration(b) displacement(c) speed(d) distance

Answer: acceleration

Solution: a = Δv/Δt, which is slope of v-t graph.

Exam Tip: Graph slope is a favorite question.

NEET Exam-style Question 4: Area under acceleration-time graph gives
(a) change in velocity(b) distance(c) position(d) speed only

Answer: change in velocity

Solution: a × t gives velocity change.

Exam Tip: Area under a-t graph is Δv.

NEET Exam-style Question 5: Retardation means
(a) acceleration opposite to velocity(b) negative velocity always(c) zero acceleration(d) increasing speed always

Answer: acceleration opposite to velocity

Solution: Retardation reduces speed.

Exam Tip: Look at direction relative to velocity.

NEET Exam-style Question 6: If u=0, v=20 m s-1, t=5 s, acceleration is
(a) 4 m s-2(b) 5 m s-2(c) 20 m s-2(d) 0

Answer: 4 m s-2

Solution: a=(20-0)/5=4.

Exam Tip: Substitute carefully.

NEET Exam-style Question 7: If velocity is constant, acceleration is
(a) zero(b) positive(c) negative(d) infinite

Answer: zero

Solution: No change in velocity means zero acceleration.

Exam Tip: Constant velocity is not accelerated motion.

NEET Exam-style Question 8: Negative acceleration with negative velocity means speed may
(a) increase(b) always decrease(c) be zero(d) not exist

Answer: increase

Solution: Acceleration and velocity in same negative direction increase speed.

Exam Tip: Retardation depends on opposite directions.

NEET Exam-style Question 9: Instantaneous acceleration is found from
(a) tangent slope of v-t graph(b) area under x-t graph(c) distance/time(d) displacement/time

Answer: tangent slope of v-t graph

Solution: Instantaneous value uses tangent slope.

Exam Tip: Tangent means instant.

NEET Exam-style Question 10: Uniform acceleration means
(a) constant acceleration(b) zero velocity(c) constant displacement(d) variable acceleration

Answer: constant acceleration

Solution: Acceleration does not change with time.

Exam Tip: Uniform acceleration gives straight v-t graph.

NEET Exam-style Question 11: Acceleration is defined as
(a) rate of change of velocity(b) rate of change of distance(c) distance/time(d) velocity/time

Answer: rate of change of velocity

Solution: a = Δv/Δt.

Exam Tip: Remember acceleration involves velocity change.

NEET Exam-style Question 12: SI unit of acceleration is
(a) m s-2(b) m s-1(c) m(d) s

Answer: m s-2

Solution: Velocity unit divided by time gives m s-2.

Exam Tip: Check units from formula.

NEET Exam-style Question 13: Slope of velocity-time graph gives
(a) acceleration(b) displacement(c) speed(d) distance

Answer: acceleration

Solution: a = Δv/Δt, which is slope of v-t graph.

Exam Tip: Graph slope is a favorite question.

NEET Exam-style Question 14: Area under acceleration-time graph gives
(a) change in velocity(b) distance(c) position(d) speed only

Answer: change in velocity

Solution: a × t gives velocity change.

Exam Tip: Area under a-t graph is Δv.

NEET Exam-style Question 15: Retardation means
(a) acceleration opposite to velocity(b) negative velocity always(c) zero acceleration(d) increasing speed always

Answer: acceleration opposite to velocity

Solution: Retardation reduces speed.

Exam Tip: Look at direction relative to velocity.

NEET Exam-style Question 16: If u=0, v=20 m s-1, t=5 s, acceleration is
(a) 4 m s-2(b) 5 m s-2(c) 20 m s-2(d) 0

Answer: 4 m s-2

Solution: a=(20-0)/5=4.

Exam Tip: Substitute carefully.

NEET Exam-style Question 17: If velocity is constant, acceleration is
(a) zero(b) positive(c) negative(d) infinite

Answer: zero

Solution: No change in velocity means zero acceleration.

Exam Tip: Constant velocity is not accelerated motion.

NEET Exam-style Question 18: Negative acceleration with negative velocity means speed may
(a) increase(b) always decrease(c) be zero(d) not exist

Answer: increase

Solution: Acceleration and velocity in same negative direction increase speed.

Exam Tip: Retardation depends on opposite directions.

NEET Exam-style Question 19: Instantaneous acceleration is found from
(a) tangent slope of v-t graph(b) area under x-t graph(c) distance/time(d) displacement/time

Answer: tangent slope of v-t graph

Solution: Instantaneous value uses tangent slope.

Exam Tip: Tangent means instant.

NEET Exam-style Question 20: Uniform acceleration means
(a) constant acceleration(b) zero velocity(c) constant displacement(d) variable acceleration

Answer: constant acceleration

Solution: Acceleration does not change with time.

Exam Tip: Uniform acceleration gives straight v-t graph.

NEET Exam-style Question 21: Acceleration is defined as
(a) rate of change of velocity(b) rate of change of distance(c) distance/time(d) velocity/time

Answer: rate of change of velocity

Solution: a = Δv/Δt.

Exam Tip: Remember acceleration involves velocity change.

NEET Exam-style Question 22: SI unit of acceleration is
(a) m s-2(b) m s-1(c) m(d) s

Answer: m s-2

Solution: Velocity unit divided by time gives m s-2.

Exam Tip: Check units from formula.

NEET Exam-style Question 23: Slope of velocity-time graph gives
(a) acceleration(b) displacement(c) speed(d) distance

Answer: acceleration

Solution: a = Δv/Δt, which is slope of v-t graph.

Exam Tip: Graph slope is a favorite question.

NEET Exam-style Question 24: Area under acceleration-time graph gives
(a) change in velocity(b) distance(c) position(d) speed only

Answer: change in velocity

Solution: a × t gives velocity change.

Exam Tip: Area under a-t graph is Δv.

NEET Exam-style Question 25: Retardation means
(a) acceleration opposite to velocity(b) negative velocity always(c) zero acceleration(d) increasing speed always

Answer: acceleration opposite to velocity

Solution: Retardation reduces speed.

Exam Tip: Look at direction relative to velocity.

NEET Exam-style Question 26: If u=0, v=20 m s-1, t=5 s, acceleration is
(a) 4 m s-2(b) 5 m s-2(c) 20 m s-2(d) 0

Answer: 4 m s-2

Solution: a=(20-0)/5=4.

Exam Tip: Substitute carefully.

NEET Exam-style Question 27: If velocity is constant, acceleration is
(a) zero(b) positive(c) negative(d) infinite

Answer: zero

Solution: No change in velocity means zero acceleration.

Exam Tip: Constant velocity is not accelerated motion.

NEET Exam-style Question 28: Negative acceleration with negative velocity means speed may
(a) increase(b) always decrease(c) be zero(d) not exist

Answer: increase

Solution: Acceleration and velocity in same negative direction increase speed.

Exam Tip: Retardation depends on opposite directions.

NEET Exam-style Question 29: Instantaneous acceleration is found from
(a) tangent slope of v-t graph(b) area under x-t graph(c) distance/time(d) displacement/time

Answer: tangent slope of v-t graph

Solution: Instantaneous value uses tangent slope.

Exam Tip: Tangent means instant.

NEET Exam-style Question 30: Uniform acceleration means
(a) constant acceleration(b) zero velocity(c) constant displacement(d) variable acceleration

Answer: constant acceleration

Solution: Acceleration does not change with time.

Exam Tip: Uniform acceleration gives straight v-t graph.

NEET Exam-style Question 31: Acceleration is defined as
(a) rate of change of velocity(b) rate of change of distance(c) distance/time(d) velocity/time

Answer: rate of change of velocity

Solution: a = Δv/Δt.

Exam Tip: Remember acceleration involves velocity change.

NEET Exam-style Question 32: SI unit of acceleration is
(a) m s-2(b) m s-1(c) m(d) s

Answer: m s-2

Solution: Velocity unit divided by time gives m s-2.

Exam Tip: Check units from formula.

NEET Exam-style Question 33: Slope of velocity-time graph gives
(a) acceleration(b) displacement(c) speed(d) distance

Answer: acceleration

Solution: a = Δv/Δt, which is slope of v-t graph.

Exam Tip: Graph slope is a favorite question.

NEET Exam-style Question 34: Area under acceleration-time graph gives
(a) change in velocity(b) distance(c) position(d) speed only

Answer: change in velocity

Solution: a × t gives velocity change.

Exam Tip: Area under a-t graph is Δv.

NEET Exam-style Question 35: Retardation means
(a) acceleration opposite to velocity(b) negative velocity always(c) zero acceleration(d) increasing speed always

Answer: acceleration opposite to velocity

Solution: Retardation reduces speed.

Exam Tip: Look at direction relative to velocity.

NEET Exam-style Question 36: If u=0, v=20 m s-1, t=5 s, acceleration is
(a) 4 m s-2(b) 5 m s-2(c) 20 m s-2(d) 0

Answer: 4 m s-2

Solution: a=(20-0)/5=4.

Exam Tip: Substitute carefully.

NEET Exam-style Question 37: If velocity is constant, acceleration is
(a) zero(b) positive(c) negative(d) infinite

Answer: zero

Solution: No change in velocity means zero acceleration.

Exam Tip: Constant velocity is not accelerated motion.

NEET Exam-style Question 38: Negative acceleration with negative velocity means speed may
(a) increase(b) always decrease(c) be zero(d) not exist

Answer: increase

Solution: Acceleration and velocity in same negative direction increase speed.

Exam Tip: Retardation depends on opposite directions.

NEET Exam-style Question 39: Instantaneous acceleration is found from
(a) tangent slope of v-t graph(b) area under x-t graph(c) distance/time(d) displacement/time

Answer: tangent slope of v-t graph

Solution: Instantaneous value uses tangent slope.

Exam Tip: Tangent means instant.

NEET Exam-style Question 40: Uniform acceleration means
(a) constant acceleration(b) zero velocity(c) constant displacement(d) variable acceleration

Answer: constant acceleration

Solution: Acceleration does not change with time.

Exam Tip: Uniform acceleration gives straight v-t graph.

NEET Exam-style Question 41: Acceleration is defined as
(a) rate of change of velocity(b) rate of change of distance(c) distance/time(d) velocity/time

Answer: rate of change of velocity

Solution: a = Δv/Δt.

Exam Tip: Remember acceleration involves velocity change.

NEET Exam-style Question 42: SI unit of acceleration is
(a) m s-2(b) m s-1(c) m(d) s

Answer: m s-2

Solution: Velocity unit divided by time gives m s-2.

Exam Tip: Check units from formula.

NEET Exam-style Question 43: Slope of velocity-time graph gives
(a) acceleration(b) displacement(c) speed(d) distance

Answer: acceleration

Solution: a = Δv/Δt, which is slope of v-t graph.

Exam Tip: Graph slope is a favorite question.

NEET Exam-style Question 44: Area under acceleration-time graph gives
(a) change in velocity(b) distance(c) position(d) speed only

Answer: change in velocity

Solution: a × t gives velocity change.

Exam Tip: Area under a-t graph is Δv.

NEET Exam-style Question 45: Retardation means
(a) acceleration opposite to velocity(b) negative velocity always(c) zero acceleration(d) increasing speed always

Answer: acceleration opposite to velocity

Solution: Retardation reduces speed.

Exam Tip: Look at direction relative to velocity.

NEET Exam-style Question 46: If u=0, v=20 m s-1, t=5 s, acceleration is
(a) 4 m s-2(b) 5 m s-2(c) 20 m s-2(d) 0

Answer: 4 m s-2

Solution: a=(20-0)/5=4.

Exam Tip: Substitute carefully.

NEET Exam-style Question 47: If velocity is constant, acceleration is
(a) zero(b) positive(c) negative(d) infinite

Answer: zero

Solution: No change in velocity means zero acceleration.

Exam Tip: Constant velocity is not accelerated motion.

NEET Exam-style Question 48: Negative acceleration with negative velocity means speed may
(a) increase(b) always decrease(c) be zero(d) not exist

Answer: increase

Solution: Acceleration and velocity in same negative direction increase speed.

Exam Tip: Retardation depends on opposite directions.

NEET Exam-style Question 49: Instantaneous acceleration is found from
(a) tangent slope of v-t graph(b) area under x-t graph(c) distance/time(d) displacement/time

Answer: tangent slope of v-t graph

Solution: Instantaneous value uses tangent slope.

Exam Tip: Tangent means instant.

NEET Exam-style Question 50: Uniform acceleration means
(a) constant acceleration(b) zero velocity(c) constant displacement(d) variable acceleration

Answer: constant acceleration

Solution: Acceleration does not change with time.

Exam Tip: Uniform acceleration gives straight v-t graph.

11. JEE Main Question Bank: 50 Questions

Authentic year is mentioned only when certain; otherwise cards are clearly marked exam-style to avoid fake PYQ years. Click a question to reveal answer.

JEE Main Exam-style Question 1: A particle velocity changes according to v=2t+3. Acceleration is?
(a) 2 m s-2(b) 3 m s-2(c) 2t(d) 5

Answer: 2 m s-2

Solution: Slope of v-t relation is 2.

Exam Tip: Linear v-t coefficient is acceleration.

JEE Main Exam-style Question 2: In a v-t graph, slope changes from positive to negative. What happens to acceleration?
(a) changes sign(b) always zero(c) always positive(d) not defined

Answer: changes sign

Solution: Acceleration is slope; slope sign changes.

Exam Tip: Graph interpretation matters.

JEE Main Exam-style Question 3: A body has velocity and acceleration in opposite directions. Speed is
(a) decreasing(b) increasing(c) constant(d) infinite

Answer: decreasing

Solution: Opposite acceleration reduces speed.

Exam Tip: This is retardation.

JEE Main Exam-style Question 4: If a-t graph area is -12 m s-1, velocity change is
(a) -12 m s-1(b) 12 m(c) -12 m s-2(d) zero

Answer: -12 m s-1

Solution: Area under acceleration-time gives Δv.

Exam Tip: Keep unit m s^-1.

JEE Main Exam-style Question 5: Uniform acceleration produces what v-t graph?
(a) straight line(b) circle(c) parabola only(d) horizontal always

Answer: straight line

Solution: Constant slope means straight line.

Exam Tip: v-t graph slope is acceleration.

JEE Main Exam-style Question 6: A particle velocity changes according to v=2t+3. Acceleration is?
(a) 2 m s-2(b) 3 m s-2(c) 2t(d) 5

Answer: 2 m s-2

Solution: Slope of v-t relation is 2.

Exam Tip: Linear v-t coefficient is acceleration.

JEE Main Exam-style Question 7: In a v-t graph, slope changes from positive to negative. What happens to acceleration?
(a) changes sign(b) always zero(c) always positive(d) not defined

Answer: changes sign

Solution: Acceleration is slope; slope sign changes.

Exam Tip: Graph interpretation matters.

JEE Main Exam-style Question 8: A body has velocity and acceleration in opposite directions. Speed is
(a) decreasing(b) increasing(c) constant(d) infinite

Answer: decreasing

Solution: Opposite acceleration reduces speed.

Exam Tip: This is retardation.

JEE Main Exam-style Question 9: If a-t graph area is -12 m s-1, velocity change is
(a) -12 m s-1(b) 12 m(c) -12 m s-2(d) zero

Answer: -12 m s-1

Solution: Area under acceleration-time gives Δv.

Exam Tip: Keep unit m s^-1.

JEE Main Exam-style Question 10: Uniform acceleration produces what v-t graph?
(a) straight line(b) circle(c) parabola only(d) horizontal always

Answer: straight line

Solution: Constant slope means straight line.

Exam Tip: v-t graph slope is acceleration.

JEE Main Exam-style Question 11: A particle velocity changes according to v=2t+3. Acceleration is?
(a) 2 m s-2(b) 3 m s-2(c) 2t(d) 5

Answer: 2 m s-2

Solution: Slope of v-t relation is 2.

Exam Tip: Linear v-t coefficient is acceleration.

JEE Main Exam-style Question 12: In a v-t graph, slope changes from positive to negative. What happens to acceleration?
(a) changes sign(b) always zero(c) always positive(d) not defined

Answer: changes sign

Solution: Acceleration is slope; slope sign changes.

Exam Tip: Graph interpretation matters.

JEE Main Exam-style Question 13: A body has velocity and acceleration in opposite directions. Speed is
(a) decreasing(b) increasing(c) constant(d) infinite

Answer: decreasing

Solution: Opposite acceleration reduces speed.

Exam Tip: This is retardation.

JEE Main Exam-style Question 14: If a-t graph area is -12 m s-1, velocity change is
(a) -12 m s-1(b) 12 m(c) -12 m s-2(d) zero

Answer: -12 m s-1

Solution: Area under acceleration-time gives Δv.

Exam Tip: Keep unit m s^-1.

JEE Main Exam-style Question 15: Uniform acceleration produces what v-t graph?
(a) straight line(b) circle(c) parabola only(d) horizontal always

Answer: straight line

Solution: Constant slope means straight line.

Exam Tip: v-t graph slope is acceleration.

JEE Main Exam-style Question 16: A particle velocity changes according to v=2t+3. Acceleration is?
(a) 2 m s-2(b) 3 m s-2(c) 2t(d) 5

Answer: 2 m s-2

Solution: Slope of v-t relation is 2.

Exam Tip: Linear v-t coefficient is acceleration.

JEE Main Exam-style Question 17: In a v-t graph, slope changes from positive to negative. What happens to acceleration?
(a) changes sign(b) always zero(c) always positive(d) not defined

Answer: changes sign

Solution: Acceleration is slope; slope sign changes.

Exam Tip: Graph interpretation matters.

JEE Main Exam-style Question 18: A body has velocity and acceleration in opposite directions. Speed is
(a) decreasing(b) increasing(c) constant(d) infinite

Answer: decreasing

Solution: Opposite acceleration reduces speed.

Exam Tip: This is retardation.

JEE Main Exam-style Question 19: If a-t graph area is -12 m s-1, velocity change is
(a) -12 m s-1(b) 12 m(c) -12 m s-2(d) zero

Answer: -12 m s-1

Solution: Area under acceleration-time gives Δv.

Exam Tip: Keep unit m s^-1.

JEE Main Exam-style Question 20: Uniform acceleration produces what v-t graph?
(a) straight line(b) circle(c) parabola only(d) horizontal always

Answer: straight line

Solution: Constant slope means straight line.

Exam Tip: v-t graph slope is acceleration.

JEE Main Exam-style Question 21: A particle velocity changes according to v=2t+3. Acceleration is?
(a) 2 m s-2(b) 3 m s-2(c) 2t(d) 5

Answer: 2 m s-2

Solution: Slope of v-t relation is 2.

Exam Tip: Linear v-t coefficient is acceleration.

JEE Main Exam-style Question 22: In a v-t graph, slope changes from positive to negative. What happens to acceleration?
(a) changes sign(b) always zero(c) always positive(d) not defined

Answer: changes sign

Solution: Acceleration is slope; slope sign changes.

Exam Tip: Graph interpretation matters.

JEE Main Exam-style Question 23: A body has velocity and acceleration in opposite directions. Speed is
(a) decreasing(b) increasing(c) constant(d) infinite

Answer: decreasing

Solution: Opposite acceleration reduces speed.

Exam Tip: This is retardation.

JEE Main Exam-style Question 24: If a-t graph area is -12 m s-1, velocity change is
(a) -12 m s-1(b) 12 m(c) -12 m s-2(d) zero

Answer: -12 m s-1

Solution: Area under acceleration-time gives Δv.

Exam Tip: Keep unit m s^-1.

JEE Main Exam-style Question 25: Uniform acceleration produces what v-t graph?
(a) straight line(b) circle(c) parabola only(d) horizontal always

Answer: straight line

Solution: Constant slope means straight line.

Exam Tip: v-t graph slope is acceleration.

JEE Main Exam-style Question 26: A particle velocity changes according to v=2t+3. Acceleration is?
(a) 2 m s-2(b) 3 m s-2(c) 2t(d) 5

Answer: 2 m s-2

Solution: Slope of v-t relation is 2.

Exam Tip: Linear v-t coefficient is acceleration.

JEE Main Exam-style Question 27: In a v-t graph, slope changes from positive to negative. What happens to acceleration?
(a) changes sign(b) always zero(c) always positive(d) not defined

Answer: changes sign

Solution: Acceleration is slope; slope sign changes.

Exam Tip: Graph interpretation matters.

JEE Main Exam-style Question 28: A body has velocity and acceleration in opposite directions. Speed is
(a) decreasing(b) increasing(c) constant(d) infinite

Answer: decreasing

Solution: Opposite acceleration reduces speed.

Exam Tip: This is retardation.

JEE Main Exam-style Question 29: If a-t graph area is -12 m s-1, velocity change is
(a) -12 m s-1(b) 12 m(c) -12 m s-2(d) zero

Answer: -12 m s-1

Solution: Area under acceleration-time gives Δv.

Exam Tip: Keep unit m s^-1.

JEE Main Exam-style Question 30: Uniform acceleration produces what v-t graph?
(a) straight line(b) circle(c) parabola only(d) horizontal always

Answer: straight line

Solution: Constant slope means straight line.

Exam Tip: v-t graph slope is acceleration.

JEE Main Exam-style Question 31: A particle velocity changes according to v=2t+3. Acceleration is?
(a) 2 m s-2(b) 3 m s-2(c) 2t(d) 5

Answer: 2 m s-2

Solution: Slope of v-t relation is 2.

Exam Tip: Linear v-t coefficient is acceleration.

JEE Main Exam-style Question 32: In a v-t graph, slope changes from positive to negative. What happens to acceleration?
(a) changes sign(b) always zero(c) always positive(d) not defined

Answer: changes sign

Solution: Acceleration is slope; slope sign changes.

Exam Tip: Graph interpretation matters.

JEE Main Exam-style Question 33: A body has velocity and acceleration in opposite directions. Speed is
(a) decreasing(b) increasing(c) constant(d) infinite

Answer: decreasing

Solution: Opposite acceleration reduces speed.

Exam Tip: This is retardation.

JEE Main Exam-style Question 34: If a-t graph area is -12 m s-1, velocity change is
(a) -12 m s-1(b) 12 m(c) -12 m s-2(d) zero

Answer: -12 m s-1

Solution: Area under acceleration-time gives Δv.

Exam Tip: Keep unit m s^-1.

JEE Main Exam-style Question 35: Uniform acceleration produces what v-t graph?
(a) straight line(b) circle(c) parabola only(d) horizontal always

Answer: straight line

Solution: Constant slope means straight line.

Exam Tip: v-t graph slope is acceleration.

JEE Main Exam-style Question 36: A particle velocity changes according to v=2t+3. Acceleration is?
(a) 2 m s-2(b) 3 m s-2(c) 2t(d) 5

Answer: 2 m s-2

Solution: Slope of v-t relation is 2.

Exam Tip: Linear v-t coefficient is acceleration.

JEE Main Exam-style Question 37: In a v-t graph, slope changes from positive to negative. What happens to acceleration?
(a) changes sign(b) always zero(c) always positive(d) not defined

Answer: changes sign

Solution: Acceleration is slope; slope sign changes.

Exam Tip: Graph interpretation matters.

JEE Main Exam-style Question 38: A body has velocity and acceleration in opposite directions. Speed is
(a) decreasing(b) increasing(c) constant(d) infinite

Answer: decreasing

Solution: Opposite acceleration reduces speed.

Exam Tip: This is retardation.

JEE Main Exam-style Question 39: If a-t graph area is -12 m s-1, velocity change is
(a) -12 m s-1(b) 12 m(c) -12 m s-2(d) zero

Answer: -12 m s-1

Solution: Area under acceleration-time gives Δv.

Exam Tip: Keep unit m s^-1.

JEE Main Exam-style Question 40: Uniform acceleration produces what v-t graph?
(a) straight line(b) circle(c) parabola only(d) horizontal always

Answer: straight line

Solution: Constant slope means straight line.

Exam Tip: v-t graph slope is acceleration.

JEE Main Exam-style Question 41: A particle velocity changes according to v=2t+3. Acceleration is?
(a) 2 m s-2(b) 3 m s-2(c) 2t(d) 5

Answer: 2 m s-2

Solution: Slope of v-t relation is 2.

Exam Tip: Linear v-t coefficient is acceleration.

JEE Main Exam-style Question 42: In a v-t graph, slope changes from positive to negative. What happens to acceleration?
(a) changes sign(b) always zero(c) always positive(d) not defined

Answer: changes sign

Solution: Acceleration is slope; slope sign changes.

Exam Tip: Graph interpretation matters.

JEE Main Exam-style Question 43: A body has velocity and acceleration in opposite directions. Speed is
(a) decreasing(b) increasing(c) constant(d) infinite

Answer: decreasing

Solution: Opposite acceleration reduces speed.

Exam Tip: This is retardation.

JEE Main Exam-style Question 44: If a-t graph area is -12 m s-1, velocity change is
(a) -12 m s-1(b) 12 m(c) -12 m s-2(d) zero

Answer: -12 m s-1

Solution: Area under acceleration-time gives Δv.

Exam Tip: Keep unit m s^-1.

JEE Main Exam-style Question 45: Uniform acceleration produces what v-t graph?
(a) straight line(b) circle(c) parabola only(d) horizontal always

Answer: straight line

Solution: Constant slope means straight line.

Exam Tip: v-t graph slope is acceleration.

JEE Main Exam-style Question 46: A particle velocity changes according to v=2t+3. Acceleration is?
(a) 2 m s-2(b) 3 m s-2(c) 2t(d) 5

Answer: 2 m s-2

Solution: Slope of v-t relation is 2.

Exam Tip: Linear v-t coefficient is acceleration.

JEE Main Exam-style Question 47: In a v-t graph, slope changes from positive to negative. What happens to acceleration?
(a) changes sign(b) always zero(c) always positive(d) not defined

Answer: changes sign

Solution: Acceleration is slope; slope sign changes.

Exam Tip: Graph interpretation matters.

JEE Main Exam-style Question 48: A body has velocity and acceleration in opposite directions. Speed is
(a) decreasing(b) increasing(c) constant(d) infinite

Answer: decreasing

Solution: Opposite acceleration reduces speed.

Exam Tip: This is retardation.

JEE Main Exam-style Question 49: If a-t graph area is -12 m s-1, velocity change is
(a) -12 m s-1(b) 12 m(c) -12 m s-2(d) zero

Answer: -12 m s-1

Solution: Area under acceleration-time gives Δv.

Exam Tip: Keep unit m s^-1.

JEE Main Exam-style Question 50: Uniform acceleration produces what v-t graph?
(a) straight line(b) circle(c) parabola only(d) horizontal always

Answer: straight line

Solution: Constant slope means straight line.

Exam Tip: v-t graph slope is acceleration.

12. JEE Advanced Question Bank: 50 Questions

Authentic year is mentioned only when certain; otherwise cards are clearly marked exam-style to avoid fake PYQ years. Click a question to reveal answer.

JEE Advanced Exam-style Question 1: A particle has v=t3-3t. Acceleration at t=2 s is?
(a) 9 m s-2(b) 6 m s-2(c) 12 m s-2(d) 3 m s-2

Answer: 9 m s-2

Solution: a=dv/dt=3t2-3; at t=2, a=12-3=9.

Exam Tip: Differentiate velocity.

JEE Advanced Exam-style Question 2: Can acceleration be non-zero at an instant when velocity is zero?
(a) Yes(b) No(c) Only in uniform speed(d) Only in circular motion

Answer: Yes

Solution: At turning point velocity may be zero but acceleration can be non-zero.

Exam Tip: Do not confuse velocity with acceleration.

JEE Advanced Exam-style Question 3: A v-t curve is concave upward. Acceleration is
(a) increasing(b) zero(c) constant negative(d) not related

Answer: increasing

Solution: Slope of v-t graph increases.

Exam Tip: Curvature shows changing acceleration.

JEE Advanced Exam-style Question 4: If acceleration depends on velocity as a=kv, what kind of acceleration is it?
(a) variable(b) uniform(c) zero(d) retardation always

Answer: variable

Solution: As velocity changes, acceleration changes.

Exam Tip: Functional dependence means variable acceleration.

JEE Advanced Exam-style Question 5: Relative acceleration of A with respect to B equals
(a) aA-aB(b) aA+aB always(c) aB-aA always(d) zero

Answer: aA-aB

Solution: Relative acceleration follows same subtraction rule.

Exam Tip: Sign convention matters.

JEE Advanced Exam-style Question 6: A particle has v=t3-3t. Acceleration at t=2 s is?
(a) 9 m s-2(b) 6 m s-2(c) 12 m s-2(d) 3 m s-2

Answer: 9 m s-2

Solution: a=dv/dt=3t2-3; at t=2, a=12-3=9.

Exam Tip: Differentiate velocity.

JEE Advanced Exam-style Question 7: Can acceleration be non-zero at an instant when velocity is zero?
(a) Yes(b) No(c) Only in uniform speed(d) Only in circular motion

Answer: Yes

Solution: At turning point velocity may be zero but acceleration can be non-zero.

Exam Tip: Do not confuse velocity with acceleration.

JEE Advanced Exam-style Question 8: A v-t curve is concave upward. Acceleration is
(a) increasing(b) zero(c) constant negative(d) not related

Answer: increasing

Solution: Slope of v-t graph increases.

Exam Tip: Curvature shows changing acceleration.

JEE Advanced Exam-style Question 9: If acceleration depends on velocity as a=kv, what kind of acceleration is it?
(a) variable(b) uniform(c) zero(d) retardation always

Answer: variable

Solution: As velocity changes, acceleration changes.

Exam Tip: Functional dependence means variable acceleration.

JEE Advanced Exam-style Question 10: Relative acceleration of A with respect to B equals
(a) aA-aB(b) aA+aB always(c) aB-aA always(d) zero

Answer: aA-aB

Solution: Relative acceleration follows same subtraction rule.

Exam Tip: Sign convention matters.

JEE Advanced Exam-style Question 11: A particle has v=t3-3t. Acceleration at t=2 s is?
(a) 9 m s-2(b) 6 m s-2(c) 12 m s-2(d) 3 m s-2

Answer: 9 m s-2

Solution: a=dv/dt=3t2-3; at t=2, a=12-3=9.

Exam Tip: Differentiate velocity.

JEE Advanced Exam-style Question 12: Can acceleration be non-zero at an instant when velocity is zero?
(a) Yes(b) No(c) Only in uniform speed(d) Only in circular motion

Answer: Yes

Solution: At turning point velocity may be zero but acceleration can be non-zero.

Exam Tip: Do not confuse velocity with acceleration.

JEE Advanced Exam-style Question 13: A v-t curve is concave upward. Acceleration is
(a) increasing(b) zero(c) constant negative(d) not related

Answer: increasing

Solution: Slope of v-t graph increases.

Exam Tip: Curvature shows changing acceleration.

JEE Advanced Exam-style Question 14: If acceleration depends on velocity as a=kv, what kind of acceleration is it?
(a) variable(b) uniform(c) zero(d) retardation always

Answer: variable

Solution: As velocity changes, acceleration changes.

Exam Tip: Functional dependence means variable acceleration.

JEE Advanced Exam-style Question 15: Relative acceleration of A with respect to B equals
(a) aA-aB(b) aA+aB always(c) aB-aA always(d) zero

Answer: aA-aB

Solution: Relative acceleration follows same subtraction rule.

Exam Tip: Sign convention matters.

JEE Advanced Exam-style Question 16: A particle has v=t3-3t. Acceleration at t=2 s is?
(a) 9 m s-2(b) 6 m s-2(c) 12 m s-2(d) 3 m s-2

Answer: 9 m s-2

Solution: a=dv/dt=3t2-3; at t=2, a=12-3=9.

Exam Tip: Differentiate velocity.

JEE Advanced Exam-style Question 17: Can acceleration be non-zero at an instant when velocity is zero?
(a) Yes(b) No(c) Only in uniform speed(d) Only in circular motion

Answer: Yes

Solution: At turning point velocity may be zero but acceleration can be non-zero.

Exam Tip: Do not confuse velocity with acceleration.

JEE Advanced Exam-style Question 18: A v-t curve is concave upward. Acceleration is
(a) increasing(b) zero(c) constant negative(d) not related

Answer: increasing

Solution: Slope of v-t graph increases.

Exam Tip: Curvature shows changing acceleration.

JEE Advanced Exam-style Question 19: If acceleration depends on velocity as a=kv, what kind of acceleration is it?
(a) variable(b) uniform(c) zero(d) retardation always

Answer: variable

Solution: As velocity changes, acceleration changes.

Exam Tip: Functional dependence means variable acceleration.

JEE Advanced Exam-style Question 20: Relative acceleration of A with respect to B equals
(a) aA-aB(b) aA+aB always(c) aB-aA always(d) zero

Answer: aA-aB

Solution: Relative acceleration follows same subtraction rule.

Exam Tip: Sign convention matters.

JEE Advanced Exam-style Question 21: A particle has v=t3-3t. Acceleration at t=2 s is?
(a) 9 m s-2(b) 6 m s-2(c) 12 m s-2(d) 3 m s-2

Answer: 9 m s-2

Solution: a=dv/dt=3t2-3; at t=2, a=12-3=9.

Exam Tip: Differentiate velocity.

JEE Advanced Exam-style Question 22: Can acceleration be non-zero at an instant when velocity is zero?
(a) Yes(b) No(c) Only in uniform speed(d) Only in circular motion

Answer: Yes

Solution: At turning point velocity may be zero but acceleration can be non-zero.

Exam Tip: Do not confuse velocity with acceleration.

JEE Advanced Exam-style Question 23: A v-t curve is concave upward. Acceleration is
(a) increasing(b) zero(c) constant negative(d) not related

Answer: increasing

Solution: Slope of v-t graph increases.

Exam Tip: Curvature shows changing acceleration.

JEE Advanced Exam-style Question 24: If acceleration depends on velocity as a=kv, what kind of acceleration is it?
(a) variable(b) uniform(c) zero(d) retardation always

Answer: variable

Solution: As velocity changes, acceleration changes.

Exam Tip: Functional dependence means variable acceleration.

JEE Advanced Exam-style Question 25: Relative acceleration of A with respect to B equals
(a) aA-aB(b) aA+aB always(c) aB-aA always(d) zero

Answer: aA-aB

Solution: Relative acceleration follows same subtraction rule.

Exam Tip: Sign convention matters.

JEE Advanced Exam-style Question 26: A particle has v=t3-3t. Acceleration at t=2 s is?
(a) 9 m s-2(b) 6 m s-2(c) 12 m s-2(d) 3 m s-2

Answer: 9 m s-2

Solution: a=dv/dt=3t2-3; at t=2, a=12-3=9.

Exam Tip: Differentiate velocity.

JEE Advanced Exam-style Question 27: Can acceleration be non-zero at an instant when velocity is zero?
(a) Yes(b) No(c) Only in uniform speed(d) Only in circular motion

Answer: Yes

Solution: At turning point velocity may be zero but acceleration can be non-zero.

Exam Tip: Do not confuse velocity with acceleration.

JEE Advanced Exam-style Question 28: A v-t curve is concave upward. Acceleration is
(a) increasing(b) zero(c) constant negative(d) not related

Answer: increasing

Solution: Slope of v-t graph increases.

Exam Tip: Curvature shows changing acceleration.

JEE Advanced Exam-style Question 29: If acceleration depends on velocity as a=kv, what kind of acceleration is it?
(a) variable(b) uniform(c) zero(d) retardation always

Answer: variable

Solution: As velocity changes, acceleration changes.

Exam Tip: Functional dependence means variable acceleration.

JEE Advanced Exam-style Question 30: Relative acceleration of A with respect to B equals
(a) aA-aB(b) aA+aB always(c) aB-aA always(d) zero

Answer: aA-aB

Solution: Relative acceleration follows same subtraction rule.

Exam Tip: Sign convention matters.

JEE Advanced Exam-style Question 31: A particle has v=t3-3t. Acceleration at t=2 s is?
(a) 9 m s-2(b) 6 m s-2(c) 12 m s-2(d) 3 m s-2

Answer: 9 m s-2

Solution: a=dv/dt=3t2-3; at t=2, a=12-3=9.

Exam Tip: Differentiate velocity.

JEE Advanced Exam-style Question 32: Can acceleration be non-zero at an instant when velocity is zero?
(a) Yes(b) No(c) Only in uniform speed(d) Only in circular motion

Answer: Yes

Solution: At turning point velocity may be zero but acceleration can be non-zero.

Exam Tip: Do not confuse velocity with acceleration.

JEE Advanced Exam-style Question 33: A v-t curve is concave upward. Acceleration is
(a) increasing(b) zero(c) constant negative(d) not related

Answer: increasing

Solution: Slope of v-t graph increases.

Exam Tip: Curvature shows changing acceleration.

JEE Advanced Exam-style Question 34: If acceleration depends on velocity as a=kv, what kind of acceleration is it?
(a) variable(b) uniform(c) zero(d) retardation always

Answer: variable

Solution: As velocity changes, acceleration changes.

Exam Tip: Functional dependence means variable acceleration.

JEE Advanced Exam-style Question 35: Relative acceleration of A with respect to B equals
(a) aA-aB(b) aA+aB always(c) aB-aA always(d) zero

Answer: aA-aB

Solution: Relative acceleration follows same subtraction rule.

Exam Tip: Sign convention matters.

JEE Advanced Exam-style Question 36: A particle has v=t3-3t. Acceleration at t=2 s is?
(a) 9 m s-2(b) 6 m s-2(c) 12 m s-2(d) 3 m s-2

Answer: 9 m s-2

Solution: a=dv/dt=3t2-3; at t=2, a=12-3=9.

Exam Tip: Differentiate velocity.

JEE Advanced Exam-style Question 37: Can acceleration be non-zero at an instant when velocity is zero?
(a) Yes(b) No(c) Only in uniform speed(d) Only in circular motion

Answer: Yes

Solution: At turning point velocity may be zero but acceleration can be non-zero.

Exam Tip: Do not confuse velocity with acceleration.

JEE Advanced Exam-style Question 38: A v-t curve is concave upward. Acceleration is
(a) increasing(b) zero(c) constant negative(d) not related

Answer: increasing

Solution: Slope of v-t graph increases.

Exam Tip: Curvature shows changing acceleration.

JEE Advanced Exam-style Question 39: If acceleration depends on velocity as a=kv, what kind of acceleration is it?
(a) variable(b) uniform(c) zero(d) retardation always

Answer: variable

Solution: As velocity changes, acceleration changes.

Exam Tip: Functional dependence means variable acceleration.

JEE Advanced Exam-style Question 40: Relative acceleration of A with respect to B equals
(a) aA-aB(b) aA+aB always(c) aB-aA always(d) zero

Answer: aA-aB

Solution: Relative acceleration follows same subtraction rule.

Exam Tip: Sign convention matters.

JEE Advanced Exam-style Question 41: A particle has v=t3-3t. Acceleration at t=2 s is?
(a) 9 m s-2(b) 6 m s-2(c) 12 m s-2(d) 3 m s-2

Answer: 9 m s-2

Solution: a=dv/dt=3t2-3; at t=2, a=12-3=9.

Exam Tip: Differentiate velocity.

JEE Advanced Exam-style Question 42: Can acceleration be non-zero at an instant when velocity is zero?
(a) Yes(b) No(c) Only in uniform speed(d) Only in circular motion

Answer: Yes

Solution: At turning point velocity may be zero but acceleration can be non-zero.

Exam Tip: Do not confuse velocity with acceleration.

JEE Advanced Exam-style Question 43: A v-t curve is concave upward. Acceleration is
(a) increasing(b) zero(c) constant negative(d) not related

Answer: increasing

Solution: Slope of v-t graph increases.

Exam Tip: Curvature shows changing acceleration.

JEE Advanced Exam-style Question 44: If acceleration depends on velocity as a=kv, what kind of acceleration is it?
(a) variable(b) uniform(c) zero(d) retardation always

Answer: variable

Solution: As velocity changes, acceleration changes.

Exam Tip: Functional dependence means variable acceleration.

JEE Advanced Exam-style Question 45: Relative acceleration of A with respect to B equals
(a) aA-aB(b) aA+aB always(c) aB-aA always(d) zero

Answer: aA-aB

Solution: Relative acceleration follows same subtraction rule.

Exam Tip: Sign convention matters.

JEE Advanced Exam-style Question 46: A particle has v=t3-3t. Acceleration at t=2 s is?
(a) 9 m s-2(b) 6 m s-2(c) 12 m s-2(d) 3 m s-2

Answer: 9 m s-2

Solution: a=dv/dt=3t2-3; at t=2, a=12-3=9.

Exam Tip: Differentiate velocity.

JEE Advanced Exam-style Question 47: Can acceleration be non-zero at an instant when velocity is zero?
(a) Yes(b) No(c) Only in uniform speed(d) Only in circular motion

Answer: Yes

Solution: At turning point velocity may be zero but acceleration can be non-zero.

Exam Tip: Do not confuse velocity with acceleration.

JEE Advanced Exam-style Question 48: A v-t curve is concave upward. Acceleration is
(a) increasing(b) zero(c) constant negative(d) not related

Answer: increasing

Solution: Slope of v-t graph increases.

Exam Tip: Curvature shows changing acceleration.

JEE Advanced Exam-style Question 49: If acceleration depends on velocity as a=kv, what kind of acceleration is it?
(a) variable(b) uniform(c) zero(d) retardation always

Answer: variable

Solution: As velocity changes, acceleration changes.

Exam Tip: Functional dependence means variable acceleration.

JEE Advanced Exam-style Question 50: Relative acceleration of A with respect to B equals
(a) aA-aB(b) aA+aB always(c) aB-aA always(d) zero

Answer: aA-aB

Solution: Relative acceleration follows same subtraction rule.

Exam Tip: Sign convention matters.

13. IB Physics Questions: 30

Click a question card to reveal answer.

IB Physics Question 1: A car velocity changes from 4 to 16 m s-1 in 6 s. Find acceleration.

Answer: 2 m s-2

Solution: (16-4)/6=2.

Exam Tip: Use change in velocity over time.

IB Physics Question 2: What does negative slope on a v-t graph mean?

Answer: Negative acceleration.

Solution: Slope of v-t graph is acceleration.

Exam Tip: Do not call it always retardation.

IB Physics Question 3: Area under acceleration-time graph gives what?

Answer: Change in velocity.

Solution: Integral/area of acceleration over time gives Δv.

Exam Tip: Remember graph-area meaning.

IB Physics Question 4: A horizontal v-t graph means?

Answer: Zero acceleration.

Solution: Velocity is constant, so acceleration is zero.

Exam Tip: Horizontal slope is zero.

IB Physics Question 5: Why is acceleration a vector?

Answer: Because velocity is vector and acceleration is rate of change of velocity.

Solution: Direction of change matters.

Exam Tip: Signs represent direction in 1D.

IB Physics Question 6: A car velocity changes from 4 to 16 m s-1 in 6 s. Find acceleration.

Answer: 2 m s-2

Solution: (16-4)/6=2.

Exam Tip: Use change in velocity over time.

IB Physics Question 7: What does negative slope on a v-t graph mean?

Answer: Negative acceleration.

Solution: Slope of v-t graph is acceleration.

Exam Tip: Do not call it always retardation.

IB Physics Question 8: Area under acceleration-time graph gives what?

Answer: Change in velocity.

Solution: Integral/area of acceleration over time gives Δv.

Exam Tip: Remember graph-area meaning.

IB Physics Question 9: A horizontal v-t graph means?

Answer: Zero acceleration.

Solution: Velocity is constant, so acceleration is zero.

Exam Tip: Horizontal slope is zero.

IB Physics Question 10: Why is acceleration a vector?

Answer: Because velocity is vector and acceleration is rate of change of velocity.

Solution: Direction of change matters.

Exam Tip: Signs represent direction in 1D.

IB Physics Question 11: A car velocity changes from 4 to 16 m s-1 in 6 s. Find acceleration.

Answer: 2 m s-2

Solution: (16-4)/6=2.

Exam Tip: Use change in velocity over time.

IB Physics Question 12: What does negative slope on a v-t graph mean?

Answer: Negative acceleration.

Solution: Slope of v-t graph is acceleration.

Exam Tip: Do not call it always retardation.

IB Physics Question 13: Area under acceleration-time graph gives what?

Answer: Change in velocity.

Solution: Integral/area of acceleration over time gives Δv.

Exam Tip: Remember graph-area meaning.

IB Physics Question 14: A horizontal v-t graph means?

Answer: Zero acceleration.

Solution: Velocity is constant, so acceleration is zero.

Exam Tip: Horizontal slope is zero.

IB Physics Question 15: Why is acceleration a vector?

Answer: Because velocity is vector and acceleration is rate of change of velocity.

Solution: Direction of change matters.

Exam Tip: Signs represent direction in 1D.

IB Physics Question 16: A car velocity changes from 4 to 16 m s-1 in 6 s. Find acceleration.

Answer: 2 m s-2

Solution: (16-4)/6=2.

Exam Tip: Use change in velocity over time.

IB Physics Question 17: What does negative slope on a v-t graph mean?

Answer: Negative acceleration.

Solution: Slope of v-t graph is acceleration.

Exam Tip: Do not call it always retardation.

IB Physics Question 18: Area under acceleration-time graph gives what?

Answer: Change in velocity.

Solution: Integral/area of acceleration over time gives Δv.

Exam Tip: Remember graph-area meaning.

IB Physics Question 19: A horizontal v-t graph means?

Answer: Zero acceleration.

Solution: Velocity is constant, so acceleration is zero.

Exam Tip: Horizontal slope is zero.

IB Physics Question 20: Why is acceleration a vector?

Answer: Because velocity is vector and acceleration is rate of change of velocity.

Solution: Direction of change matters.

Exam Tip: Signs represent direction in 1D.

IB Physics Question 21: A car velocity changes from 4 to 16 m s-1 in 6 s. Find acceleration.

Answer: 2 m s-2

Solution: (16-4)/6=2.

Exam Tip: Use change in velocity over time.

IB Physics Question 22: What does negative slope on a v-t graph mean?

Answer: Negative acceleration.

Solution: Slope of v-t graph is acceleration.

Exam Tip: Do not call it always retardation.

IB Physics Question 23: Area under acceleration-time graph gives what?

Answer: Change in velocity.

Solution: Integral/area of acceleration over time gives Δv.

Exam Tip: Remember graph-area meaning.

IB Physics Question 24: A horizontal v-t graph means?

Answer: Zero acceleration.

Solution: Velocity is constant, so acceleration is zero.

Exam Tip: Horizontal slope is zero.

IB Physics Question 25: Why is acceleration a vector?

Answer: Because velocity is vector and acceleration is rate of change of velocity.

Solution: Direction of change matters.

Exam Tip: Signs represent direction in 1D.

IB Physics Question 26: A car velocity changes from 4 to 16 m s-1 in 6 s. Find acceleration.

Answer: 2 m s-2

Solution: (16-4)/6=2.

Exam Tip: Use change in velocity over time.

IB Physics Question 27: What does negative slope on a v-t graph mean?

Answer: Negative acceleration.

Solution: Slope of v-t graph is acceleration.

Exam Tip: Do not call it always retardation.

IB Physics Question 28: Area under acceleration-time graph gives what?

Answer: Change in velocity.

Solution: Integral/area of acceleration over time gives Δv.

Exam Tip: Remember graph-area meaning.

IB Physics Question 29: A horizontal v-t graph means?

Answer: Zero acceleration.

Solution: Velocity is constant, so acceleration is zero.

Exam Tip: Horizontal slope is zero.

IB Physics Question 30: Why is acceleration a vector?

Answer: Because velocity is vector and acceleration is rate of change of velocity.

Solution: Direction of change matters.

Exam Tip: Signs represent direction in 1D.

14. IGCSE Questions: 30

Click a question card to reveal answer.

IGCSE Question 1: Define acceleration.

Answer: Rate of change of velocity.

Solution: Acceleration = change in velocity/time.

Exam Tip: Use correct unit.

IGCSE Question 2: State SI unit of acceleration.

Answer: m s-2.

Solution: Velocity unit m s^-1 divided by second.

Exam Tip: Do not write m/s only.

IGCSE Question 3: A bicycle slows down. What is the acceleration called?

Answer: Retardation or deceleration.

Solution: Acceleration is opposite to velocity.

Exam Tip: Retardation is a magnitude.

IGCSE Question 4: What does a straight rising v-t graph show?

Answer: Uniform positive acceleration.

Solution: Slope is constant and positive.

Exam Tip: Straight line means constant acceleration.

IGCSE Question 5: If speed is constant, is acceleration always zero?

Answer: In straight-line motion, yes if direction is constant.

Solution: Velocity is unchanged.

Exam Tip: For curved motion, direction can change.

IGCSE Question 6: Define acceleration.

Answer: Rate of change of velocity.

Solution: Acceleration = change in velocity/time.

Exam Tip: Use correct unit.

IGCSE Question 7: State SI unit of acceleration.

Answer: m s-2.

Solution: Velocity unit m s^-1 divided by second.

Exam Tip: Do not write m/s only.

IGCSE Question 8: A bicycle slows down. What is the acceleration called?

Answer: Retardation or deceleration.

Solution: Acceleration is opposite to velocity.

Exam Tip: Retardation is a magnitude.

IGCSE Question 9: What does a straight rising v-t graph show?

Answer: Uniform positive acceleration.

Solution: Slope is constant and positive.

Exam Tip: Straight line means constant acceleration.

IGCSE Question 10: If speed is constant, is acceleration always zero?

Answer: In straight-line motion, yes if direction is constant.

Solution: Velocity is unchanged.

Exam Tip: For curved motion, direction can change.

IGCSE Question 11: Define acceleration.

Answer: Rate of change of velocity.

Solution: Acceleration = change in velocity/time.

Exam Tip: Use correct unit.

IGCSE Question 12: State SI unit of acceleration.

Answer: m s-2.

Solution: Velocity unit m s^-1 divided by second.

Exam Tip: Do not write m/s only.

IGCSE Question 13: A bicycle slows down. What is the acceleration called?

Answer: Retardation or deceleration.

Solution: Acceleration is opposite to velocity.

Exam Tip: Retardation is a magnitude.

IGCSE Question 14: What does a straight rising v-t graph show?

Answer: Uniform positive acceleration.

Solution: Slope is constant and positive.

Exam Tip: Straight line means constant acceleration.

IGCSE Question 15: If speed is constant, is acceleration always zero?

Answer: In straight-line motion, yes if direction is constant.

Solution: Velocity is unchanged.

Exam Tip: For curved motion, direction can change.

IGCSE Question 16: Define acceleration.

Answer: Rate of change of velocity.

Solution: Acceleration = change in velocity/time.

Exam Tip: Use correct unit.

IGCSE Question 17: State SI unit of acceleration.

Answer: m s-2.

Solution: Velocity unit m s^-1 divided by second.

Exam Tip: Do not write m/s only.

IGCSE Question 18: A bicycle slows down. What is the acceleration called?

Answer: Retardation or deceleration.

Solution: Acceleration is opposite to velocity.

Exam Tip: Retardation is a magnitude.

IGCSE Question 19: What does a straight rising v-t graph show?

Answer: Uniform positive acceleration.

Solution: Slope is constant and positive.

Exam Tip: Straight line means constant acceleration.

IGCSE Question 20: If speed is constant, is acceleration always zero?

Answer: In straight-line motion, yes if direction is constant.

Solution: Velocity is unchanged.

Exam Tip: For curved motion, direction can change.

IGCSE Question 21: Define acceleration.

Answer: Rate of change of velocity.

Solution: Acceleration = change in velocity/time.

Exam Tip: Use correct unit.

IGCSE Question 22: State SI unit of acceleration.

Answer: m s-2.

Solution: Velocity unit m s^-1 divided by second.

Exam Tip: Do not write m/s only.

IGCSE Question 23: A bicycle slows down. What is the acceleration called?

Answer: Retardation or deceleration.

Solution: Acceleration is opposite to velocity.

Exam Tip: Retardation is a magnitude.

IGCSE Question 24: What does a straight rising v-t graph show?

Answer: Uniform positive acceleration.

Solution: Slope is constant and positive.

Exam Tip: Straight line means constant acceleration.

IGCSE Question 25: If speed is constant, is acceleration always zero?

Answer: In straight-line motion, yes if direction is constant.

Solution: Velocity is unchanged.

Exam Tip: For curved motion, direction can change.

IGCSE Question 26: Define acceleration.

Answer: Rate of change of velocity.

Solution: Acceleration = change in velocity/time.

Exam Tip: Use correct unit.

IGCSE Question 27: State SI unit of acceleration.

Answer: m s-2.

Solution: Velocity unit m s^-1 divided by second.

Exam Tip: Do not write m/s only.

IGCSE Question 28: A bicycle slows down. What is the acceleration called?

Answer: Retardation or deceleration.

Solution: Acceleration is opposite to velocity.

Exam Tip: Retardation is a magnitude.

IGCSE Question 29: What does a straight rising v-t graph show?

Answer: Uniform positive acceleration.

Solution: Slope is constant and positive.

Exam Tip: Straight line means constant acceleration.

IGCSE Question 30: If speed is constant, is acceleration always zero?

Answer: In straight-line motion, yes if direction is constant.

Solution: Velocity is unchanged.

Exam Tip: For curved motion, direction can change.

15. A-Level Questions: 30

Click a question card to reveal answer.

A-Level Question 1: For v=5t2, find acceleration at t=3 s.

Answer: 30 m s-2.

Solution: a=dv/dt=10t, so a=30.

Exam Tip: Differentiate for instantaneous acceleration.

A-Level Question 2: What is relative acceleration?

Answer: Acceleration of one body as measured from another.

Solution: aAB=aA-aB.

Exam Tip: Use vector subtraction.

A-Level Question 3: How is displacement found from v-t graph under acceleration?

Answer: Area under v-t graph.

Solution: Area represents integral of velocity over time.

Exam Tip: Use geometry for straight-line graphs.

A-Level Question 4: When can negative acceleration increase speed?

Answer: When velocity is also negative.

Solution: Acceleration and velocity same direction increases speed.

Exam Tip: Retardation requires opposite direction.

A-Level Question 5: What does variable acceleration imply on v-t graph?

Answer: Changing slope.

Solution: Acceleration is slope of v-t graph.

Exam Tip: Curved v-t graph means variable acceleration.

A-Level Question 6: For v=5t2, find acceleration at t=3 s.

Answer: 30 m s-2.

Solution: a=dv/dt=10t, so a=30.

Exam Tip: Differentiate for instantaneous acceleration.

A-Level Question 7: What is relative acceleration?

Answer: Acceleration of one body as measured from another.

Solution: aAB=aA-aB.

Exam Tip: Use vector subtraction.

A-Level Question 8: How is displacement found from v-t graph under acceleration?

Answer: Area under v-t graph.

Solution: Area represents integral of velocity over time.

Exam Tip: Use geometry for straight-line graphs.

A-Level Question 9: When can negative acceleration increase speed?

Answer: When velocity is also negative.

Solution: Acceleration and velocity same direction increases speed.

Exam Tip: Retardation requires opposite direction.

A-Level Question 10: What does variable acceleration imply on v-t graph?

Answer: Changing slope.

Solution: Acceleration is slope of v-t graph.

Exam Tip: Curved v-t graph means variable acceleration.

A-Level Question 11: For v=5t2, find acceleration at t=3 s.

Answer: 30 m s-2.

Solution: a=dv/dt=10t, so a=30.

Exam Tip: Differentiate for instantaneous acceleration.

A-Level Question 12: What is relative acceleration?

Answer: Acceleration of one body as measured from another.

Solution: aAB=aA-aB.

Exam Tip: Use vector subtraction.

A-Level Question 13: How is displacement found from v-t graph under acceleration?

Answer: Area under v-t graph.

Solution: Area represents integral of velocity over time.

Exam Tip: Use geometry for straight-line graphs.

A-Level Question 14: When can negative acceleration increase speed?

Answer: When velocity is also negative.

Solution: Acceleration and velocity same direction increases speed.

Exam Tip: Retardation requires opposite direction.

A-Level Question 15: What does variable acceleration imply on v-t graph?

Answer: Changing slope.

Solution: Acceleration is slope of v-t graph.

Exam Tip: Curved v-t graph means variable acceleration.

A-Level Question 16: For v=5t2, find acceleration at t=3 s.

Answer: 30 m s-2.

Solution: a=dv/dt=10t, so a=30.

Exam Tip: Differentiate for instantaneous acceleration.

A-Level Question 17: What is relative acceleration?

Answer: Acceleration of one body as measured from another.

Solution: aAB=aA-aB.

Exam Tip: Use vector subtraction.

A-Level Question 18: How is displacement found from v-t graph under acceleration?

Answer: Area under v-t graph.

Solution: Area represents integral of velocity over time.

Exam Tip: Use geometry for straight-line graphs.

A-Level Question 19: When can negative acceleration increase speed?

Answer: When velocity is also negative.

Solution: Acceleration and velocity same direction increases speed.

Exam Tip: Retardation requires opposite direction.

A-Level Question 20: What does variable acceleration imply on v-t graph?

Answer: Changing slope.

Solution: Acceleration is slope of v-t graph.

Exam Tip: Curved v-t graph means variable acceleration.

A-Level Question 21: For v=5t2, find acceleration at t=3 s.

Answer: 30 m s-2.

Solution: a=dv/dt=10t, so a=30.

Exam Tip: Differentiate for instantaneous acceleration.

A-Level Question 22: What is relative acceleration?

Answer: Acceleration of one body as measured from another.

Solution: aAB=aA-aB.

Exam Tip: Use vector subtraction.

A-Level Question 23: How is displacement found from v-t graph under acceleration?

Answer: Area under v-t graph.

Solution: Area represents integral of velocity over time.

Exam Tip: Use geometry for straight-line graphs.

A-Level Question 24: When can negative acceleration increase speed?

Answer: When velocity is also negative.

Solution: Acceleration and velocity same direction increases speed.

Exam Tip: Retardation requires opposite direction.

A-Level Question 25: What does variable acceleration imply on v-t graph?

Answer: Changing slope.

Solution: Acceleration is slope of v-t graph.

Exam Tip: Curved v-t graph means variable acceleration.

A-Level Question 26: For v=5t2, find acceleration at t=3 s.

Answer: 30 m s-2.

Solution: a=dv/dt=10t, so a=30.

Exam Tip: Differentiate for instantaneous acceleration.

A-Level Question 27: What is relative acceleration?

Answer: Acceleration of one body as measured from another.

Solution: aAB=aA-aB.

Exam Tip: Use vector subtraction.

A-Level Question 28: How is displacement found from v-t graph under acceleration?

Answer: Area under v-t graph.

Solution: Area represents integral of velocity over time.

Exam Tip: Use geometry for straight-line graphs.

A-Level Question 29: When can negative acceleration increase speed?

Answer: When velocity is also negative.

Solution: Acceleration and velocity same direction increases speed.

Exam Tip: Retardation requires opposite direction.

A-Level Question 30: What does variable acceleration imply on v-t graph?

Answer: Changing slope.

Solution: Acceleration is slope of v-t graph.

Exam Tip: Curved v-t graph means variable acceleration.

16. Assertion Reason Questions

Options: (a) Both A and R are true and R explains A. (b) Both true but R does not explain A. (c) A true, R false. (d) A false, R true. Click to reveal.

Assertion Reason 1: Assertion: Acceleration is a vector quantity. Reason: It is the rate of change of velocity, and velocity is a vector.

Answer: (a)

Solution: Both true and reason explains assertion.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 2: Assertion: Retardation always means negative acceleration. Reason: Retardation means acceleration opposite to velocity.

Answer: (d)

Solution: Assertion false; sign depends on chosen direction.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 3: Assertion: Slope of v-t graph gives acceleration. Reason: Acceleration equals change in velocity per unit time.

Answer: (a)

Solution: Correct.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 4: Assertion: Area under a-t graph gives displacement. Reason: Acceleration integrated over time gives change in velocity.

Answer: (d)

Solution: Assertion false, reason true.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 5: Assertion: A body can have zero velocity and non-zero acceleration. Reason: At a turning point, velocity may vanish while acceleration remains.

Answer: (a)

Solution: Correct.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 6: Assertion: Uniform acceleration gives straight line v-t graph. Reason: A straight v-t graph has constant slope.

Answer: (a)

Solution: Correct.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 7: Assertion: Negative acceleration always decreases speed. Reason: Speed decreases only when acceleration is opposite to velocity.

Answer: (d)

Solution: Assertion false, reason true.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 8: Assertion: Instantaneous acceleration is tangent slope on v-t graph. Reason: Tangent gives local rate of change.

Answer: (a)

Solution: Correct.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 9: Assertion: Zero acceleration means velocity is constant. Reason: No change in velocity means acceleration is zero.

Answer: (a)

Solution: Correct.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 10: Assertion: Variable acceleration means acceleration is zero. Reason: Variable acceleration changes with time or state.

Answer: (d)

Solution: Assertion false, reason true.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 11: Assertion: Acceleration is a vector quantity. Reason: It is the rate of change of velocity, and velocity is a vector.

Answer: (a)

Solution: Both true and reason explains assertion.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 12: Assertion: Retardation always means negative acceleration. Reason: Retardation means acceleration opposite to velocity.

Answer: (d)

Solution: Assertion false; sign depends on chosen direction.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 13: Assertion: Slope of v-t graph gives acceleration. Reason: Acceleration equals change in velocity per unit time.

Answer: (a)

Solution: Correct.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 14: Assertion: Area under a-t graph gives displacement. Reason: Acceleration integrated over time gives change in velocity.

Answer: (d)

Solution: Assertion false, reason true.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 15: Assertion: A body can have zero velocity and non-zero acceleration. Reason: At a turning point, velocity may vanish while acceleration remains.

Answer: (a)

Solution: Correct.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 16: Assertion: Uniform acceleration gives straight line v-t graph. Reason: A straight v-t graph has constant slope.

Answer: (a)

Solution: Correct.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 17: Assertion: Negative acceleration always decreases speed. Reason: Speed decreases only when acceleration is opposite to velocity.

Answer: (d)

Solution: Assertion false, reason true.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 18: Assertion: Instantaneous acceleration is tangent slope on v-t graph. Reason: Tangent gives local rate of change.

Answer: (a)

Solution: Correct.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 19: Assertion: Zero acceleration means velocity is constant. Reason: No change in velocity means acceleration is zero.

Answer: (a)

Solution: Correct.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 20: Assertion: Variable acceleration means acceleration is zero. Reason: Variable acceleration changes with time or state.

Answer: (d)

Solution: Assertion false, reason true.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 21: Assertion: Acceleration is a vector quantity. Reason: It is the rate of change of velocity, and velocity is a vector.

Answer: (a)

Solution: Both true and reason explains assertion.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 22: Assertion: Retardation always means negative acceleration. Reason: Retardation means acceleration opposite to velocity.

Answer: (d)

Solution: Assertion false; sign depends on chosen direction.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 23: Assertion: Slope of v-t graph gives acceleration. Reason: Acceleration equals change in velocity per unit time.

Answer: (a)

Solution: Correct.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 24: Assertion: Area under a-t graph gives displacement. Reason: Acceleration integrated over time gives change in velocity.

Answer: (d)

Solution: Assertion false, reason true.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 25: Assertion: A body can have zero velocity and non-zero acceleration. Reason: At a turning point, velocity may vanish while acceleration remains.

Answer: (a)

Solution: Correct.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 26: Assertion: Uniform acceleration gives straight line v-t graph. Reason: A straight v-t graph has constant slope.

Answer: (a)

Solution: Correct.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 27: Assertion: Negative acceleration always decreases speed. Reason: Speed decreases only when acceleration is opposite to velocity.

Answer: (d)

Solution: Assertion false, reason true.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 28: Assertion: Instantaneous acceleration is tangent slope on v-t graph. Reason: Tangent gives local rate of change.

Answer: (a)

Solution: Correct.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 29: Assertion: Zero acceleration means velocity is constant. Reason: No change in velocity means acceleration is zero.

Answer: (a)

Solution: Correct.

Exam Tip: Check whether assertion and reason are independently true.

Assertion Reason 30: Assertion: Variable acceleration means acceleration is zero. Reason: Variable acceleration changes with time or state.

Answer: (d)

Solution: Assertion false, reason true.

Exam Tip: Check whether assertion and reason are independently true.

17. Case Study Questions

Click case cards to reveal answers.

Case Study 1: Car Braking: A car moving at 25 m s-1 brakes uniformly and stops in 5 s. Questions: Find acceleration; identify retardation; explain graph; state sign convention.

Answer: a=(0-25)/5=-5 m s-2; retardation=5 m s-2; v-t graph slopes downward; positive direction is initial motion.

Solution: Apply acceleration formula, sign convention and graph interpretation.

Exam Tip: Read the passage first, then identify velocity change and direction.

Case Study 2: Train Acceleration: A train starts from rest and reaches 30 m s-1 in 60 s. Questions: Find acceleration; is it uniform?; graph type; velocity after 30 s.

Answer: a=0.5 m s-2; if stated uniform yes; v-t graph straight rising; v=15 m s-1.

Solution: Apply acceleration formula, sign convention and graph interpretation.

Exam Tip: Read the passage first, then identify velocity change and direction.

Case Study 3: Rocket Launch: A rocket velocity increases rapidly and acceleration may change with time. Questions: Is acceleration constant?; what graph shows this?; what does area under a-t give?; why variable?

Answer: Not necessarily; curved v-t or changing a-t graph; change in velocity; thrust and mass change.

Solution: Apply acceleration formula, sign convention and graph interpretation.

Exam Tip: Read the passage first, then identify velocity change and direction.

Case Study 4: Free Fall: A ball thrown upward has acceleration due to gravity downward throughout motion. Questions: Acceleration sign if upward positive?; velocity at top?; acceleration at top?; is upward motion retarded?

Answer: a=-g; velocity zero at top; acceleration=-g; yes speed decreases while moving upward.

Solution: Apply acceleration formula, sign convention and graph interpretation.

Exam Tip: Read the passage first, then identify velocity change and direction.

Case Study 5: Velocity-Time Graph: A v-t graph has positive slope, then horizontal part, then negative slope. Questions: Identify acceleration in each region; where is acceleration zero?; where is retardation possible?; what does area give?

Answer: Positive, zero, negative; horizontal part; negative slope if velocity positive; displacement.

Solution: Apply acceleration formula, sign convention and graph interpretation.

Exam Tip: Read the passage first, then identify velocity change and direction.

Case Study 6: Motion Sensor Data: A sensor records velocity every second and values are not equally spaced. Questions: What does unequal change show?; how to find average acceleration?; how to estimate instantaneous acceleration?; graph needed?

Answer: Variable acceleration; Δv/Δt over interval; tangent slope; yes v-t graph helps.

Solution: Apply acceleration formula, sign convention and graph interpretation.

Exam Tip: Read the passage first, then identify velocity change and direction.

18. Interactive Question Mode

All NEET, JEE Main, JEE Advanced, Assertion Reason and Case Study questions above use pure HTML/CSS collapsible cards. Initially only the question is visible. Click the card or the Show Answer label to expand the solution.

19. Quick Revision Notes

Formula Sheet

  • a = Δv / Δt
  • a = (vf - vi) / Δt
  • Slope of v-t graph = acceleration
  • Area under a-t graph = Δv

Acceleration vs Retardation

  • Acceleration is vector.
  • Negative acceleration depends on sign convention.
  • Retardation means speed decreases.
  • Retardation is opposite to velocity.

Common Mistakes

  • Calling every negative acceleration retardation.
  • Ignoring signs of velocity.
  • Using v/t instead of Δv/Δt.
  • Confusing v-t slope with area.
Last-minute tip: first decide direction, then write initial velocity, final velocity and time before applying a=(v-u)/t.

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