CLASS 11 PHYSICS • MOTION IN A STRAIGHT LINE

Speed and Velocity

Understand speed, velocity, average motion, instantaneous motion and relative velocity with NEET, JEE and CBSE level numericals.

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1. Speed

Speed tells how fast an object covers distance. It is a scalar quantity, so it has magnitude only and no direction. Speed is always positive or zero.

Speed = Distance / Time

Scalar Nature

Only magnitude matters. A car moving at 60 km h^-1 has speed 60 km h^-1.

SI Unit

The SI unit of speed is m s^-1.

Daily Life

Speedometer, running pace and train speed are common examples.

2. Average Speed

Average speed is total distance divided by total time. It does not care about direction or displacement.

Average Speed = Total Distance / Total Time

Equal Time Trick

If equal time is spent at speeds v₁ and v₂, average speed = (v₁ + v₂) / 2.

Equal Distance Trick

If equal distances are covered at speeds v₁ and v₂, average speed = 2v₁v₂ / (v₁ + v₂).

Multi-stage Journey

Add all distances and divide by total time. Never average speeds directly unless time intervals are equal.

Solved Example: Equal Distance

Question: A car covers half distance at 40 km h^-1 and half at 60 km h^-1. Find average speed.

Given: v₁=40, v₂=60, equal distances.

Formula: v_avg = 2v₁v₂/(v₁+v₂)

Substitution: 2×40×60/(40+60)

Calculation: 4800/100 = 48 km h^-1

Final Answer: 48 km h^-1

Exam Tip: For equal distances use harmonic mean, not arithmetic mean.

Solved Example: Equal Time

Question: A cyclist moves 10 m s^-1 for 5 s and 20 m s^-1 for 5 s. Find average speed.

Given: Equal times.

Formula: v_avg = (v₁+v₂)/2

Substitution: (10+20)/2

Calculation: 15 m s^-1

Final Answer: 15 m s^-1

Exam Tip: Arithmetic mean works only for equal time intervals.

3. Instantaneous Speed

Instantaneous speed is speed at a particular instant. A speedometer shows instantaneous speed. In a distance-time graph, it is the magnitude of slope at that instant.

4. Velocity

Velocity is rate of change of displacement. It is a vector quantity, so direction matters. In one-dimensional motion, sign represents direction.

Velocity = Displacement / Time

Positive Velocity

Motion in chosen positive direction.

Negative Velocity

Motion opposite to chosen positive direction.

Zero Velocity

Position is not changing at that instant.

5. Average Velocity

Average velocity is total displacement divided by total time. It can be zero even when average speed is non-zero.

Average Velocity = Total Displacement / Total Time

Zero Average Velocity Example

Question: A runner completes one round of a circular track in 100 s. Find average speed and average velocity if track circumference is 400 m.

Given: Distance = 400 m, displacement = 0, time = 100 s.

Formula: Average speed = distance/time; average velocity = displacement/time

Substitution: 400/100 and 0/100

Calculation: Average speed = 4 m s^-1, average velocity = 0

Final Answer: 4 m s^-1, 0

Exam Tip: Round trip gives zero average velocity.

Negative Displacement Example

Question: A particle moves from x = 10 m to x = -5 m in 3 s. Find average velocity.

Given: x₁=10 m, x₂=-5 m, t=3 s.

Formula: v_avg = (x₂-x₁)/t

Substitution: (-5-10)/3

Calculation: -15/3 = -5 m s^-1

Final Answer: -5 m s^-1

Exam Tip: Sign of velocity shows direction.

6. Instantaneous Velocity

Instantaneous velocity is velocity at an instant, including direction. It is the slope of the position-time graph at that instant.

Positive Slope

Positive velocity.

Negative Slope

Negative velocity.

Zero Slope

Zero velocity at that instant.

IIT/JEE concept: a particle can have zero instantaneous velocity at a turning point even though it has travelled non-zero distance earlier.

7. Speed vs Velocity

Point	Speed	Velocity
Definition	Distance per unit time.	Displacement per unit time.
Nature	Scalar.	Vector.
Formula	speed = distance / time	velocity = displacement / time
Sign	Never negative.	Positive, negative or zero.
Path Dependence	Depends on path.	Depends on displacement.
Direction	No direction.	Direction matters.
Can be zero?	Yes, if object is at rest.	Yes, if displacement change is zero or instantaneous slope is zero.
Graph Meaning	Slope of distance-time graph.	Slope of position-time graph.

8. Relative Velocity — Very Important

Relative velocity means velocity of one object as seen by another object. Direction and sign convention are essential.

v_AB = v_A - v_B

Same Direction

v_relative = |v₁ - v₂|

Opposite Direction

v_relative = v₁ + v₂

Time to Meet

t = separation / relative speed

Two runners towards each other

Question: Two runners 100 m apart run towards each other at 6 m s^-1 and 4 m s^-1. Find meeting time.

Given: separation=100 m, speeds 6 and 4.

Formula: t = separation/(v₁+v₂)

Substitution: 100/(6+4)

Calculation: 10 s

Final Answer: 10 s

Exam Tip: Towards each other means relative speed is sum.

Same direction trains

Question: Train A at 30 m s^-1 overtakes train B at 20 m s^-1. Relative speed?

Given: same direction.

Formula: v_rel = |v₁-v₂|

Substitution: |30-20|

Calculation: 10 m s^-1

Final Answer: 10 m s^-1

Exam Tip: Overtaking uses difference of speeds.

Opposite direction trains

Question: Two trains move opposite at 18 m s^-1 and 22 m s^-1. Find relative speed.

Given: opposite directions.

Formula: v_rel = v₁+v₂

Substitution: 18+22

Calculation: 40 m s^-1

Final Answer: 40 m s^-1

Exam Tip: Opposite direction means add.

Train crossing platform

Question: A 150 m train moving 15 m s^-1 crosses a 300 m platform. Find time.

Given: total length = 150+300 = 450 m.

Formula: time = total length/speed

Substitution: 450/15

Calculation: 30 s

Final Answer: 30 s

Exam Tip: For platform, train covers train length plus platform length.

9. Rain and Umbrella Problems

Rain problems use relative velocity of rain with respect to person.

v_rain,person = v_rain - v_person

Rain Example 1

Question: Rain falls vertically at 10 m s^-1 and a man walks horizontally at 5 m s^-1. Find apparent speed and umbrella angle from vertical.

Given: v_rain=10, v_man=5.

Formula: v_apparent = √(v_rain² + v_man²), tan θ = v_man/v_rain

Substitution: √(10²+5²), tan θ=5/10

Calculation: v=11.18 m s^-1, θ=26.6°

Final Answer: 11.18 m s^-1, 26.6° from vertical

Exam Tip: Hold umbrella opposite to apparent rain direction.

Rain Example 2

Question: Rain falls vertically at 12 m s^-1 and a man walks horizontally at 5 m s^-1. Find apparent speed and umbrella angle from vertical.

Given: v_rain=12, v_man=5.

Formula: v_apparent = √(v_rain² + v_man²), tan θ = v_man/v_rain

Substitution: √(12²+5²), tan θ=5/12

Calculation: v=13.0 m s^-1, θ=22.6°

Final Answer: 13.0 m s^-1, 22.6° from vertical

Exam Tip: Hold umbrella opposite to apparent rain direction.

Rain Example 3

Question: Rain falls vertically at 15 m s^-1 and a man walks horizontally at 10 m s^-1. Find apparent speed and umbrella angle from vertical.

Given: v_rain=15, v_man=10.

Formula: v_apparent = √(v_rain² + v_man²), tan θ = v_man/v_rain

Substitution: √(15²+10²), tan θ=10/15

Calculation: v=18.03 m s^-1, θ=33.7°

Final Answer: 18.03 m s^-1, 33.7° from vertical

Exam Tip: Hold umbrella opposite to apparent rain direction.

Rain Example 4

Question: Rain falls vertically at 20 m s^-1 and a man walks horizontally at 15 m s^-1. Find apparent speed and umbrella angle from vertical.

Given: v_rain=20, v_man=15.

Formula: v_apparent = √(v_rain² + v_man²), tan θ = v_man/v_rain

Substitution: √(20²+15²), tan θ=15/20

Calculation: v=25.0 m s^-1, θ=36.9°

Final Answer: 25.0 m s^-1, 36.9° from vertical

Exam Tip: Hold umbrella opposite to apparent rain direction.

Rain Example 5

Question: Rain falls vertically at 8 m s^-1 and a man walks horizontally at 6 m s^-1. Find apparent speed and umbrella angle from vertical.

Given: v_rain=8, v_man=6.

Formula: v_apparent = √(v_rain² + v_man²), tan θ = v_man/v_rain

Substitution: √(8²+6²), tan θ=6/8

Calculation: v=10.0 m s^-1, θ=36.9°

Final Answer: 10.0 m s^-1, 36.9° from vertical

Exam Tip: Hold umbrella opposite to apparent rain direction.

Rain Example 6

Question: Rain falls vertically at 24 m s^-1 and a man walks horizontally at 7 m s^-1. Find apparent speed and umbrella angle from vertical.

Given: v_rain=24, v_man=7.

Formula: v_apparent = √(v_rain² + v_man²), tan θ = v_man/v_rain

Substitution: √(24²+7²), tan θ=7/24

Calculation: v=25.0 m s^-1, θ=16.3°

Final Answer: 25.0 m s^-1, 16.3° from vertical

Exam Tip: Hold umbrella opposite to apparent rain direction.

Rain Example 7

Question: Rain falls vertically at 18 m s^-1 and a man walks horizontally at 12 m s^-1. Find apparent speed and umbrella angle from vertical.

Given: v_rain=18, v_man=12.

Formula: v_apparent = √(v_rain² + v_man²), tan θ = v_man/v_rain

Substitution: √(18²+12²), tan θ=12/18

Calculation: v=21.63 m s^-1, θ=33.7°

Final Answer: 21.63 m s^-1, 33.7° from vertical

Exam Tip: Hold umbrella opposite to apparent rain direction.

Rain Example 8

Question: Rain falls vertically at 30 m s^-1 and a man walks horizontally at 16 m s^-1. Find apparent speed and umbrella angle from vertical.

Given: v_rain=30, v_man=16.

Formula: v_apparent = √(v_rain² + v_man²), tan θ = v_man/v_rain

Substitution: √(30²+16²), tan θ=16/30

Calculation: v=34.0 m s^-1, θ=28.1°

Final Answer: 34.0 m s^-1, 28.1° from vertical

Exam Tip: Hold umbrella opposite to apparent rain direction.

10. River Boat Problems

Shortest time: aim perpendicular to bank. Shortest path: aim upstream so resultant velocity is perpendicular to bank.

River Boat Example 1

Question: River width is 120 m, boat speed in still water 6 m s^-1, river speed 2 m s^-1. If boat is aimed perpendicular to bank, find crossing time and drift.

Given: Boat aimed perpendicular.

Formula: t = width/v_boat, drift = v_rivert

Substitution: t=120/6, drift=2×20.0

Calculation: t=20.0 s, drift=40.0 m

Final Answer: 20.0 s, 40.0 m

Exam Tip: Perpendicular aiming gives shortest time, not shortest path.

River Boat Example 2

Question: River width is 200 m, boat speed in still water 10 m s^-1, river speed 5 m s^-1. If boat is aimed perpendicular to bank, find crossing time and drift.

Given: Boat aimed perpendicular.

Formula: t = width/v_boat, drift = v_rivert

Substitution: t=200/10, drift=5×20.0

Calculation: t=20.0 s, drift=100.0 m

Final Answer: 20.0 s, 100.0 m

Exam Tip: Perpendicular aiming gives shortest time, not shortest path.

River Boat Example 3

Question: River width is 300 m, boat speed in still water 15 m s^-1, river speed 9 m s^-1. If boat is aimed perpendicular to bank, find crossing time and drift.

Given: Boat aimed perpendicular.

Formula: t = width/v_boat, drift = v_rivert

Substitution: t=300/15, drift=9×20.0

Calculation: t=20.0 s, drift=180.0 m

Final Answer: 20.0 s, 180.0 m

Exam Tip: Perpendicular aiming gives shortest time, not shortest path.

River Boat Example 4

Question: River width is 80 m, boat speed in still water 4 m s^-1, river speed 3 m s^-1. If boat is aimed perpendicular to bank, find crossing time and drift.

Given: Boat aimed perpendicular.

Formula: t = width/v_boat, drift = v_rivert

Substitution: t=80/4, drift=3×20.0

Calculation: t=20.0 s, drift=60.0 m

Final Answer: 20.0 s, 60.0 m

Exam Tip: Perpendicular aiming gives shortest time, not shortest path.

River Boat Example 5

Question: River width is 150 m, boat speed in still water 5 m s^-1, river speed 4 m s^-1. If boat is aimed perpendicular to bank, find crossing time and drift.

Given: Boat aimed perpendicular.

Formula: t = width/v_boat, drift = v_rivert

Substitution: t=150/5, drift=4×30.0

Calculation: t=30.0 s, drift=120.0 m

Final Answer: 30.0 s, 120.0 m

Exam Tip: Perpendicular aiming gives shortest time, not shortest path.

River Boat Example 6

Question: River width is 240 m, boat speed in still water 12 m s^-1, river speed 5 m s^-1. If boat is aimed perpendicular to bank, find crossing time and drift.

Given: Boat aimed perpendicular.

Formula: t = width/v_boat, drift = v_rivert

Substitution: t=240/12, drift=5×20.0

Calculation: t=20.0 s, drift=100.0 m

Final Answer: 20.0 s, 100.0 m

Exam Tip: Perpendicular aiming gives shortest time, not shortest path.

River Boat Example 7

Question: River width is 100 m, boat speed in still water 8 m s^-1, river speed 6 m s^-1. If boat is aimed perpendicular to bank, find crossing time and drift.

Given: Boat aimed perpendicular.

Formula: t = width/v_boat, drift = v_rivert

Substitution: t=100/8, drift=6×12.5

Calculation: t=12.5 s, drift=75.0 m

Final Answer: 12.5 s, 75.0 m

Exam Tip: Perpendicular aiming gives shortest time, not shortest path.

River Boat Example 8

Question: River width is 180 m, boat speed in still water 9 m s^-1, river speed 3 m s^-1. If boat is aimed perpendicular to bank, find crossing time and drift.

Given: Boat aimed perpendicular.

Formula: t = width/v_boat, drift = v_rivert

Substitution: t=180/9, drift=3×20.0

Calculation: t=20.0 s, drift=60.0 m

Final Answer: 20.0 s, 60.0 m

Exam Tip: Perpendicular aiming gives shortest time, not shortest path.

River Boat Example 9

Question: River width is 360 m, boat speed in still water 18 m s^-1, river speed 6 m s^-1. If boat is aimed perpendicular to bank, find crossing time and drift.

Given: Boat aimed perpendicular.

Formula: t = width/v_boat, drift = v_rivert

Substitution: t=360/18, drift=6×20.0

Calculation: t=20.0 s, drift=120.0 m

Final Answer: 20.0 s, 120.0 m

Exam Tip: Perpendicular aiming gives shortest time, not shortest path.

River Boat Example 10

Question: River width is 90 m, boat speed in still water 5 m s^-1, river speed 1 m s^-1. If boat is aimed perpendicular to bank, find crossing time and drift.

Given: Boat aimed perpendicular.

Formula: t = width/v_boat, drift = v_rivert

Substitution: t=90/5, drift=1×18.0

Calculation: t=18.0 s, drift=18.0 m

Final Answer: 18.0 s, 18.0 m

Exam Tip: Perpendicular aiming gives shortest time, not shortest path.

River Boat Example 11

Question: River width is 250 m, boat speed in still water 10 m s^-1, river speed 6 m s^-1. If boat is aimed perpendicular to bank, find crossing time and drift.

Given: Boat aimed perpendicular.

Formula: t = width/v_boat, drift = v_rivert

Substitution: t=250/10, drift=6×25.0

Calculation: t=25.0 s, drift=150.0 m

Final Answer: 25.0 s, 150.0 m

Exam Tip: Perpendicular aiming gives shortest time, not shortest path.

River Boat Example 12

Question: River width is 400 m, boat speed in still water 20 m s^-1, river speed 12 m s^-1. If boat is aimed perpendicular to bank, find crossing time and drift.

Given: Boat aimed perpendicular.

Formula: t = width/v_boat, drift = v_rivert

Substitution: t=400/20, drift=12×20.0

Calculation: t=20.0 s, drift=240.0 m

Final Answer: 20.0 s, 240.0 m

Exam Tip: Perpendicular aiming gives shortest time, not shortest path.

Shortest path trick: aim upstream so horizontal component of boat velocity cancels river current.

11. Bird Between Car and Wall / Train Type Problems

Find total time first, then multiply by bird speed.

Bird Shuttle Example 1

Question: A car is 100 m from a wall and moves toward it at 10 m s^-1. A bird flies between car and wall at 20 m s^-1 until collision. Find bird distance.

Given: separation, car speed, bird speed given.

Formula: time before collision = separation/car speed; bird distance = bird speed × time

Substitution: t=100/10; distance=20×10

Calculation: t=10 s, distance=200 m

Final Answer: 200 m

Exam Tip: Do not count trips; use total time.

Bird Shuttle Example 2

Question: A car is 200 m from a wall and moves toward it at 20 m s^-1. A bird flies between car and wall at 30 m s^-1 until collision. Find bird distance.

Given: separation, car speed, bird speed given.

Formula: time before collision = separation/car speed; bird distance = bird speed × time

Substitution: t=200/20; distance=30×10

Calculation: t=10 s, distance=300 m

Final Answer: 300 m

Exam Tip: Do not count trips; use total time.

Bird Shuttle Example 3

Question: A car is 150 m from a wall and moves toward it at 15 m s^-1. A bird flies between car and wall at 25 m s^-1 until collision. Find bird distance.

Given: separation, car speed, bird speed given.

Formula: time before collision = separation/car speed; bird distance = bird speed × time

Substitution: t=150/15; distance=25×10

Calculation: t=10 s, distance=250 m

Final Answer: 250 m

Exam Tip: Do not count trips; use total time.

Bird Shuttle Example 4

Question: A car is 300 m from a wall and moves toward it at 30 m s^-1. A bird flies between car and wall at 40 m s^-1 until collision. Find bird distance.

Given: separation, car speed, bird speed given.

Formula: time before collision = separation/car speed; bird distance = bird speed × time

Substitution: t=300/30; distance=40×10

Calculation: t=10 s, distance=400 m

Final Answer: 400 m

Exam Tip: Do not count trips; use total time.

Bird Shuttle Example 5

Question: A car is 120 m from a wall and moves toward it at 12 m s^-1. A bird flies between car and wall at 18 m s^-1 until collision. Find bird distance.

Given: separation, car speed, bird speed given.

Formula: time before collision = separation/car speed; bird distance = bird speed × time

Substitution: t=120/12; distance=18×10

Calculation: t=10 s, distance=180 m

Final Answer: 180 m

Exam Tip: Do not count trips; use total time.

Bird Shuttle Example 6

Question: A car is 500 m from a wall and moves toward it at 25 m s^-1. A bird flies between car and wall at 50 m s^-1 until collision. Find bird distance.

Given: separation, car speed, bird speed given.

Formula: time before collision = separation/car speed; bird distance = bird speed × time

Substitution: t=500/25; distance=50×20

Calculation: t=20 s, distance=1000 m

Final Answer: 1000 m

Exam Tip: Do not count trips; use total time.

12. Chasing Problems

In symmetric chasing, particles meet at the centre. The path is curved but symmetry makes the meeting point simple.

Square Chasing Problem

Question: Four persons at corners of a square of side a run with speed v, each chasing the next person. Find meeting time.

Given: side = a, speed = v.

Formula: Component of velocity towards centre = v cos 45° = v/√2; distance to centre = a/√2.

Substitution: t = (a/√2)/(v/√2)

Calculation: t = a/v

Final Answer: a/v

Exam Tip: Symmetry reduces the curved path problem.

Triangle Chasing Problem

Question: Three persons at corners of an equilateral triangle of side a run with speed v, each chasing the next. Find meeting time.

Given: equilateral triangle side a.

Formula: component toward centre = v cos 30°, distance to centre = a/√3.

Substitution: t=(a/√3)/(v√3/2)

Calculation: t = 2a/(3v)

Final Answer: 2a/(3v)

Exam Tip: Use centre distance and radial component.

General Polygon

Question: N particles at regular polygon vertices chase next particle with speed v. What is the meeting point?

Given: Regular polygon and equal speeds.

Formula: By symmetry, all meet at centre.

Substitution: All remain symmetrically placed during motion.

Calculation: Meeting point is centre.

Final Answer: Centre

Exam Tip: Symmetry is the key concept.

13. Graph-Based Speed and Velocity

Slope of position-time gives velocity. Slope of distance-time gives speed. Area under velocity-time gives displacement.

Graph Example 1

Question: In an x-t graph, position changes from 2 m to 14 m in 3 s. Find average velocity.

Given: x₁=2 m, x₂=14 m, t=3 s.

Formula: v_avg = Δx/Δt

Substitution: (14-2)/3

Calculation: 4 m s^-1

Final Answer: 4 m s^-1

Exam Tip: Slope of x-t graph is velocity.

Graph Example 2

Question: In a v-t graph, velocity is 10 m s^-1 for 5 s. Find displacement.

Given: v=10, t=5.

Formula: Displacement = area under v-t graph

Substitution: 10×5

Calculation: 50 m

Final Answer: 50 m

Exam Tip: Area under v-t graph gives displacement.

14. Important Numerical Types

Average Speed

Question: A body covers 100 m in 10 s and 100 m in 20 s. Find average speed.

Given: Total distance=200 m, total time=30 s.

Formula: v_avg=total distance/total time

Substitution: 200/30

Calculation: 6.67 m s^-1

Final Answer: 6.67 m s^-1

Exam Tip: Do not average 10 and 5 directly unless times equal.

Train Crossing

Question: A train of length 180 m crosses a pole in 12 s. Find speed.

Given: length=180 m, time=12 s.

Formula: speed=distance/time

Substitution: 180/12

Calculation: 15 m s^-1

Final Answer: 15 m s^-1

Exam Tip: For pole, distance equals train length.

Relative Velocity

Question: Two cars move same direction at 25 and 15 m s^-1. Relative speed?

Given: same direction.

Formula: v_rel=difference

Substitution: 25-15

Calculation: 10 m s^-1

Final Answer: 10 m s^-1

Exam Tip: Same direction means subtract.

Graph Velocity

Question: Position changes from -4 m to +8 m in 6 s. Average velocity?

Given: Δx=12 m, t=6 s.

Formula: v=Δx/t

Substitution: 12/6

Calculation: 2 m s^-1

Final Answer: 2 m s^-1

Exam Tip: Use displacement, not distance, for velocity.

15. NEET Question Bank: 60 MCQs

Year labels are used only when authentic year is certain. The following are clearly marked NEET Exam-style Question to avoid fake PYQ years.

NEET Exam-style Question 1

Question: Average speed is defined as

(a) total distance / total time(b) displacement / time(c) velocity / time(d) acceleration × time

Correct Answer: total distance / total time

Detailed Solution: Average speed uses total path length.

Exam Tip: Speed uses distance.

NEET Exam-style Question 2

Question: Average velocity is defined as

(a) total displacement / total time(b) total distance / total time(c) speed × time(d) distance × time

Correct Answer: total displacement / total time

Detailed Solution: Velocity uses displacement.

Exam Tip: Direction matters.

NEET Exam-style Question 3

Question: Speed is

(a) scalar(b) vector(c) always negative(d) direction only

Correct Answer: scalar

Detailed Solution: Speed has magnitude only.

Exam Tip: No direction for speed.

NEET Exam-style Question 4

Question: Velocity can be

(a) positive, negative or zero(b) only positive(c) only negative(d) never zero

Correct Answer: positive, negative or zero

Detailed Solution: Velocity sign depends on direction.

Exam Tip: Use sign convention.

NEET Exam-style Question 5

Question: If equal distances are covered at v₁ and v₂, average speed is

(a) 2v₁v₂/(v₁+v₂)(b) (v₁+v₂)/2(c) v₁-v₂(d) v₁+v₂

Correct Answer: 2v₁v₂/(v₁+v₂)

Detailed Solution: Equal distance uses harmonic mean.

Exam Tip: Classic NEET trick.

NEET Exam-style Question 6

Question: Same direction relative speed equals

(a) |v₁-v₂|(b) v₁+v₂(c) v₁v₂(d) zero always

Correct Answer: |v₁-v₂|

Detailed Solution: Same direction means subtract speeds.

Exam Tip: Overtaking uses difference.

NEET Exam-style Question 7

Question: Opposite direction relative speed equals

(a) v₁+v₂(b) |v₁-v₂|(c) v₁/v₂(d) zero

Correct Answer: v₁+v₂

Detailed Solution: Opposite direction means add.

Exam Tip: Meeting/crossing uses sum.

NEET Exam-style Question 8

Question: For shortest time in river crossing, boat should be aimed

(a) perpendicular to bank(b) upstream angle(c) downstream angle(d) parallel to bank

Correct Answer: perpendicular to bank

Detailed Solution: The across-river component is maximum.

Exam Tip: Shortest time ignores drift.

NEET Exam-style Question 9

Question: In bird shuttle problem, first find

(a) total time before collision(b) number of trips(c) average acceleration(d) river speed

Correct Answer: total time before collision

Detailed Solution: Bird distance = bird speed × total time.

Exam Tip: Do not count trips.

NEET Exam-style Question 10

Question: In x-t graph, slope gives

(a) velocity(b) distance(c) speed only(d) acceleration

Correct Answer: velocity

Detailed Solution: Slope of position-time graph is velocity.

Exam Tip: Sign of slope matters.

NEET Exam-style Question 11

Question: Average speed is defined as

(a) total distance / total time(b) displacement / time(c) velocity / time(d) acceleration × time

Correct Answer: total distance / total time

Detailed Solution: Average speed uses total path length.

Exam Tip: Speed uses distance.

NEET Exam-style Question 12

Question: Average velocity is defined as

(a) total displacement / total time(b) total distance / total time(c) speed × time(d) distance × time

Correct Answer: total displacement / total time

Detailed Solution: Velocity uses displacement.

Exam Tip: Direction matters.

NEET Exam-style Question 13

Question: Speed is

(a) scalar(b) vector(c) always negative(d) direction only

Correct Answer: scalar

Detailed Solution: Speed has magnitude only.

Exam Tip: No direction for speed.

NEET Exam-style Question 14

Question: Velocity can be

(a) positive, negative or zero(b) only positive(c) only negative(d) never zero

Correct Answer: positive, negative or zero

Detailed Solution: Velocity sign depends on direction.

Exam Tip: Use sign convention.

NEET Exam-style Question 15

Question: If equal distances are covered at v₁ and v₂, average speed is

(a) 2v₁v₂/(v₁+v₂)(b) (v₁+v₂)/2(c) v₁-v₂(d) v₁+v₂

Correct Answer: 2v₁v₂/(v₁+v₂)

Detailed Solution: Equal distance uses harmonic mean.

Exam Tip: Classic NEET trick.

NEET Exam-style Question 16

Question: Same direction relative speed equals

(a) |v₁-v₂|(b) v₁+v₂(c) v₁v₂(d) zero always

Correct Answer: |v₁-v₂|

Detailed Solution: Same direction means subtract speeds.

Exam Tip: Overtaking uses difference.

NEET Exam-style Question 17

Question: Opposite direction relative speed equals

(a) v₁+v₂(b) |v₁-v₂|(c) v₁/v₂(d) zero

Correct Answer: v₁+v₂

Detailed Solution: Opposite direction means add.

Exam Tip: Meeting/crossing uses sum.

NEET Exam-style Question 18

Question: For shortest time in river crossing, boat should be aimed

(a) perpendicular to bank(b) upstream angle(c) downstream angle(d) parallel to bank

Correct Answer: perpendicular to bank

Detailed Solution: The across-river component is maximum.

Exam Tip: Shortest time ignores drift.

NEET Exam-style Question 19

Question: In bird shuttle problem, first find

(a) total time before collision(b) number of trips(c) average acceleration(d) river speed

Correct Answer: total time before collision

Detailed Solution: Bird distance = bird speed × total time.

Exam Tip: Do not count trips.

NEET Exam-style Question 20

Question: In x-t graph, slope gives

(a) velocity(b) distance(c) speed only(d) acceleration

Correct Answer: velocity

Detailed Solution: Slope of position-time graph is velocity.

Exam Tip: Sign of slope matters.

NEET Exam-style Question 21

Question: Average speed is defined as

(a) total distance / total time(b) displacement / time(c) velocity / time(d) acceleration × time

Correct Answer: total distance / total time

Detailed Solution: Average speed uses total path length.

Exam Tip: Speed uses distance.

NEET Exam-style Question 22

Question: Average velocity is defined as

(a) total displacement / total time(b) total distance / total time(c) speed × time(d) distance × time

Correct Answer: total displacement / total time

Detailed Solution: Velocity uses displacement.

Exam Tip: Direction matters.

NEET Exam-style Question 23

Question: Speed is

(a) scalar(b) vector(c) always negative(d) direction only

Correct Answer: scalar

Detailed Solution: Speed has magnitude only.

Exam Tip: No direction for speed.

NEET Exam-style Question 24

Question: Velocity can be

(a) positive, negative or zero(b) only positive(c) only negative(d) never zero

Correct Answer: positive, negative or zero

Detailed Solution: Velocity sign depends on direction.

Exam Tip: Use sign convention.

NEET Exam-style Question 25

Question: If equal distances are covered at v₁ and v₂, average speed is

(a) 2v₁v₂/(v₁+v₂)(b) (v₁+v₂)/2(c) v₁-v₂(d) v₁+v₂

Correct Answer: 2v₁v₂/(v₁+v₂)

Detailed Solution: Equal distance uses harmonic mean.

Exam Tip: Classic NEET trick.

NEET Exam-style Question 26

Question: Same direction relative speed equals

(a) |v₁-v₂|(b) v₁+v₂(c) v₁v₂(d) zero always

Correct Answer: |v₁-v₂|

Detailed Solution: Same direction means subtract speeds.

Exam Tip: Overtaking uses difference.

NEET Exam-style Question 27

Question: Opposite direction relative speed equals

(a) v₁+v₂(b) |v₁-v₂|(c) v₁/v₂(d) zero

Correct Answer: v₁+v₂

Detailed Solution: Opposite direction means add.

Exam Tip: Meeting/crossing uses sum.

NEET Exam-style Question 28

Question: For shortest time in river crossing, boat should be aimed

(a) perpendicular to bank(b) upstream angle(c) downstream angle(d) parallel to bank

Correct Answer: perpendicular to bank

Detailed Solution: The across-river component is maximum.

Exam Tip: Shortest time ignores drift.

NEET Exam-style Question 29

Question: In bird shuttle problem, first find

(a) total time before collision(b) number of trips(c) average acceleration(d) river speed

Correct Answer: total time before collision

Detailed Solution: Bird distance = bird speed × total time.

Exam Tip: Do not count trips.

NEET Exam-style Question 30

Question: In x-t graph, slope gives

(a) velocity(b) distance(c) speed only(d) acceleration

Correct Answer: velocity

Detailed Solution: Slope of position-time graph is velocity.

Exam Tip: Sign of slope matters.

NEET Exam-style Question 31

Question: Average speed is defined as

(a) total distance / total time(b) displacement / time(c) velocity / time(d) acceleration × time

Correct Answer: total distance / total time

Detailed Solution: Average speed uses total path length.

Exam Tip: Speed uses distance.

NEET Exam-style Question 32

Question: Average velocity is defined as

(a) total displacement / total time(b) total distance / total time(c) speed × time(d) distance × time

Correct Answer: total displacement / total time

Detailed Solution: Velocity uses displacement.

Exam Tip: Direction matters.

NEET Exam-style Question 33

Question: Speed is

(a) scalar(b) vector(c) always negative(d) direction only

Correct Answer: scalar

Detailed Solution: Speed has magnitude only.

Exam Tip: No direction for speed.

NEET Exam-style Question 34

Question: Velocity can be

(a) positive, negative or zero(b) only positive(c) only negative(d) never zero

Correct Answer: positive, negative or zero

Detailed Solution: Velocity sign depends on direction.

Exam Tip: Use sign convention.

NEET Exam-style Question 35

Question: If equal distances are covered at v₁ and v₂, average speed is

(a) 2v₁v₂/(v₁+v₂)(b) (v₁+v₂)/2(c) v₁-v₂(d) v₁+v₂

Correct Answer: 2v₁v₂/(v₁+v₂)

Detailed Solution: Equal distance uses harmonic mean.

Exam Tip: Classic NEET trick.

NEET Exam-style Question 36

Question: Same direction relative speed equals

(a) |v₁-v₂|(b) v₁+v₂(c) v₁v₂(d) zero always

Correct Answer: |v₁-v₂|

Detailed Solution: Same direction means subtract speeds.

Exam Tip: Overtaking uses difference.

NEET Exam-style Question 37

Question: Opposite direction relative speed equals

(a) v₁+v₂(b) |v₁-v₂|(c) v₁/v₂(d) zero

Correct Answer: v₁+v₂

Detailed Solution: Opposite direction means add.

Exam Tip: Meeting/crossing uses sum.

NEET Exam-style Question 38

Question: For shortest time in river crossing, boat should be aimed

(a) perpendicular to bank(b) upstream angle(c) downstream angle(d) parallel to bank

Correct Answer: perpendicular to bank

Detailed Solution: The across-river component is maximum.

Exam Tip: Shortest time ignores drift.

NEET Exam-style Question 39

Question: In bird shuttle problem, first find

(a) total time before collision(b) number of trips(c) average acceleration(d) river speed

Correct Answer: total time before collision

Detailed Solution: Bird distance = bird speed × total time.

Exam Tip: Do not count trips.

NEET Exam-style Question 40

Question: In x-t graph, slope gives

(a) velocity(b) distance(c) speed only(d) acceleration

Correct Answer: velocity

Detailed Solution: Slope of position-time graph is velocity.

Exam Tip: Sign of slope matters.

NEET Exam-style Question 41

Question: Average speed is defined as

(a) total distance / total time(b) displacement / time(c) velocity / time(d) acceleration × time

Correct Answer: total distance / total time

Detailed Solution: Average speed uses total path length.

Exam Tip: Speed uses distance.

NEET Exam-style Question 42

Question: Average velocity is defined as

(a) total displacement / total time(b) total distance / total time(c) speed × time(d) distance × time

Correct Answer: total displacement / total time

Detailed Solution: Velocity uses displacement.

Exam Tip: Direction matters.

NEET Exam-style Question 43

Question: Speed is

(a) scalar(b) vector(c) always negative(d) direction only

Correct Answer: scalar

Detailed Solution: Speed has magnitude only.

Exam Tip: No direction for speed.

NEET Exam-style Question 44

Question: Velocity can be

(a) positive, negative or zero(b) only positive(c) only negative(d) never zero

Correct Answer: positive, negative or zero

Detailed Solution: Velocity sign depends on direction.

Exam Tip: Use sign convention.

NEET Exam-style Question 45

Question: If equal distances are covered at v₁ and v₂, average speed is

(a) 2v₁v₂/(v₁+v₂)(b) (v₁+v₂)/2(c) v₁-v₂(d) v₁+v₂

Correct Answer: 2v₁v₂/(v₁+v₂)

Detailed Solution: Equal distance uses harmonic mean.

Exam Tip: Classic NEET trick.

NEET Exam-style Question 46

Question: Same direction relative speed equals

(a) |v₁-v₂|(b) v₁+v₂(c) v₁v₂(d) zero always

Correct Answer: |v₁-v₂|

Detailed Solution: Same direction means subtract speeds.

Exam Tip: Overtaking uses difference.

NEET Exam-style Question 47

Question: Opposite direction relative speed equals

(a) v₁+v₂(b) |v₁-v₂|(c) v₁/v₂(d) zero

Correct Answer: v₁+v₂

Detailed Solution: Opposite direction means add.

Exam Tip: Meeting/crossing uses sum.

NEET Exam-style Question 48

Question: For shortest time in river crossing, boat should be aimed

(a) perpendicular to bank(b) upstream angle(c) downstream angle(d) parallel to bank

Correct Answer: perpendicular to bank

Detailed Solution: The across-river component is maximum.

Exam Tip: Shortest time ignores drift.

NEET Exam-style Question 49

Question: In bird shuttle problem, first find

(a) total time before collision(b) number of trips(c) average acceleration(d) river speed

Correct Answer: total time before collision

Detailed Solution: Bird distance = bird speed × total time.

Exam Tip: Do not count trips.

NEET Exam-style Question 50

Question: In x-t graph, slope gives

(a) velocity(b) distance(c) speed only(d) acceleration

Correct Answer: velocity

Detailed Solution: Slope of position-time graph is velocity.

Exam Tip: Sign of slope matters.

NEET Exam-style Question 51

Question: Average speed is defined as

(a) total distance / total time(b) displacement / time(c) velocity / time(d) acceleration × time

Correct Answer: total distance / total time

Detailed Solution: Average speed uses total path length.

Exam Tip: Speed uses distance.

NEET Exam-style Question 52

Question: Average velocity is defined as

(a) total displacement / total time(b) total distance / total time(c) speed × time(d) distance × time

Correct Answer: total displacement / total time

Detailed Solution: Velocity uses displacement.

Exam Tip: Direction matters.

NEET Exam-style Question 53

Question: Speed is

(a) scalar(b) vector(c) always negative(d) direction only

Correct Answer: scalar

Detailed Solution: Speed has magnitude only.

Exam Tip: No direction for speed.

NEET Exam-style Question 54

Question: Velocity can be

(a) positive, negative or zero(b) only positive(c) only negative(d) never zero

Correct Answer: positive, negative or zero

Detailed Solution: Velocity sign depends on direction.

Exam Tip: Use sign convention.

NEET Exam-style Question 55

Question: If equal distances are covered at v₁ and v₂, average speed is

(a) 2v₁v₂/(v₁+v₂)(b) (v₁+v₂)/2(c) v₁-v₂(d) v₁+v₂

Correct Answer: 2v₁v₂/(v₁+v₂)

Detailed Solution: Equal distance uses harmonic mean.

Exam Tip: Classic NEET trick.

NEET Exam-style Question 56

Question: Same direction relative speed equals

(a) |v₁-v₂|(b) v₁+v₂(c) v₁v₂(d) zero always

Correct Answer: |v₁-v₂|

Detailed Solution: Same direction means subtract speeds.

Exam Tip: Overtaking uses difference.

NEET Exam-style Question 57

Question: Opposite direction relative speed equals

(a) v₁+v₂(b) |v₁-v₂|(c) v₁/v₂(d) zero

Correct Answer: v₁+v₂

Detailed Solution: Opposite direction means add.

Exam Tip: Meeting/crossing uses sum.

NEET Exam-style Question 58

Question: For shortest time in river crossing, boat should be aimed

(a) perpendicular to bank(b) upstream angle(c) downstream angle(d) parallel to bank

Correct Answer: perpendicular to bank

Detailed Solution: The across-river component is maximum.

Exam Tip: Shortest time ignores drift.

NEET Exam-style Question 59

Question: In bird shuttle problem, first find

(a) total time before collision(b) number of trips(c) average acceleration(d) river speed

Correct Answer: total time before collision

Detailed Solution: Bird distance = bird speed × total time.

Exam Tip: Do not count trips.

NEET Exam-style Question 60

Given: x=3t².

Formula: v = change rate of x = 6t

Substitution: 6×2

Calculation: 12 m s^-1

Final Answer: 12 m s^-1

Exam Tip: Instantaneous velocity is slope of x-t curve.

17. JEE Advanced Questions

JEE Advanced Exam-style Question

Question: Four particles at square corners chase next with speed v. Find meeting time for side a.

Given: square symmetry.

Formula: t=a/v

Substitution: radial component method

Calculation: a/v

Final Answer: a/v

Exam Tip: Curved path but symmetric meeting at centre.

JEE Advanced Exam-style Question

Question: Three particles at equilateral triangle corners chase next with speed v. Find meeting time.

Given: side a.

Formula: t = 2a/(3v)

Substitution: centre distance divided by radial component

Calculation: 2a/(3v)

Final Answer: 2a/(3v)

Exam Tip: Use cos 30° component.

JEE Advanced Exam-style Question

Question: A boat must cross river with no drift. Boat speed b, river speed r. Find upstream angle with perpendicular.

Given: b>r.

Formula: b sin θ = r

Substitution: sin θ = r/b

Calculation: θ = sin^-1(r/b)

Final Answer: θ = sin^-1(r/b)

Exam Tip: For shortest path, cancel current.

JEE Advanced Exam-style Question

Question: Can instantaneous speed be positive while instantaneous velocity is negative?

Given: 1D motion opposite positive direction.

Formula: speed = magnitude of velocity

Substitution: velocity negative, speed positive

Calculation: yes

Final Answer: Yes

Exam Tip: Speed is magnitude of velocity.

18. CBSE Questions

1 Mark

Question: Define speed.

Answer: Distance travelled per unit time.

2 Mark

Question: Differentiate speed and velocity.

Answer: Speed is scalar and uses distance; velocity is vector and uses displacement.

3 Mark

Question: Why can average velocity be zero while average speed is not zero?

Answer: In a round trip, displacement is zero but distance is non-zero.

5 Mark

Question: Explain relative velocity with same and opposite direction examples.

Answer: Same direction relative speed is difference; opposite direction relative speed is sum.

19. IB / IGCSE / A-Level Questions

IB Physics 1

Question: Explain average velocity from displacement-time data.

Answer: Average velocity = change in displacement / time interval.

IB Physics 2

Question: What does area under velocity-time graph give?

Answer: Displacement.

IB Physics 3

Question: Why is velocity vector?

Answer: It includes direction.

IGCSE Physics 1

Question: State SI unit of speed.

Answer: m s^-1.

IGCSE Physics 2

Question: How is speed measured in daily life?

Answer: Using speedometer or distance/time.

IGCSE Physics 3

Question: What does a horizontal distance-time graph mean?

Answer: Object is at rest.

A-Level Physics 1

Question: Find relative velocity formula.

Answer: v_AB=v_A-v_B.

A-Level Physics 2

Answer: (a)

Explanation: Correct.

Assertion Reason 30

Assertion: Instantaneous speed is magnitude of instantaneous velocity.

Reason: Speed has no direction.

Answer: (a)

Explanation: Correct.

21. Case Study Questions

Case Study: Train Journey

Two trains move on parallel tracks and a passenger observes relative motion.

Questions: Same direction formula?; Opposite direction formula?; What length is crossed?; Why use relative speed?

Answers: Difference; sum; combined lengths for train-train crossing; relative motion changes frame.

Explanation: The case applies speed, velocity and relative motion formulas in exam-style context.

Case Study: River Boat

A boat crosses a flowing river and drifts downstream.

Questions: Shortest time direction?; Cause of drift?; How to get shortest path?; What is resultant velocity?

Answers: Perpendicular to bank; river current; aim upstream; vector sum of boat and river velocities.

Explanation: The case applies speed, velocity and relative motion formulas in exam-style context.

Case Study: Rain and Umbrella

A person walks east while rain falls vertically.

Questions: Why rain appears slant?; Which velocity is used?; Umbrella direction?; What increases apparent angle?

Answers: Relative velocity; rain relative to person; opposite apparent rain; greater walking speed.

Explanation: The case applies speed, velocity and relative motion formulas in exam-style context.

Case Study: Bird between Car and Wall

A bird flies between a car and wall repeatedly until car reaches wall.

Questions: First step?; Bird distance formula?; Need number of trips?; Why?

Answers: Find collision time; bird speed × time; no; trips become infinite-like but total time finite.

Explanation: The case applies speed, velocity and relative motion formulas in exam-style context.

Case Study: Chasing on Square

Four persons chase next person from square corners.

Questions: Meeting point?; Time?; Path shape?; Key idea?

Answers: Centre; a/v; curved; symmetry.

Explanation: The case applies speed, velocity and relative motion formulas in exam-style context.

Case Study: Chasing on Triangle

Three persons chase next person from equilateral triangle corners.

Questions: Meeting point?; Time?; Component used?; Key idea?

Answers: Centre; 2a/(3v); radial component v cos30°; symmetry.

Explanation: The case applies speed, velocity and relative motion formulas in exam-style context.

Case Study: Motion Graphs

A position-time graph has positive, zero and negative slopes.

Questions: Positive slope means?; Zero slope means?; Negative slope means?; Area under v-t means?

Answers: Positive velocity; zero velocity; negative velocity; displacement.

Explanation: The case applies speed, velocity and relative motion formulas in exam-style context.

22. Quick Revision Notes

Formula Sheet

Speed = distance/time
Velocity = displacement/time
v_AB = v_A - v_B
Same direction: |v₁-v₂|
Opposite direction: v₁+v₂

Problem Tricks

River shortest time: aim perpendicular.
River shortest path: aim upstream.
Bird shuttle: distance = bird speed × total time.
Rain: use relative velocity.
Train crossing: add required lengths.

Common Mistakes

Averaging speeds directly in equal-distance problems.
Using distance for velocity.
Forgetting sign of velocity.
Using actual rain instead of apparent rain.
Counting bird trips instead of total time.

Last-minute tip: identify whether the question asks for distance, displacement, speed, velocity or relative velocity before substituting values.

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