CLASS 11 PHYSICS • MOTION IN A STRAIGHT LINE

Position, Distance and Displacement

Master reference frames, position coordinates, distance, displacement, sign convention, graphical understanding and exam numericals.

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1. Reference Frame

A reference frame is a coordinate system or observer from which position and motion are described. Motion has meaning only after choosing a reference frame.

Stationary Frame

A frame attached to ground, road, classroom or platform. A car moving on road changes position with respect to this frame.

Moving Frame

A frame attached to a moving train, bus or lift. A passenger sitting inside a train may be at rest in train frame but moving in ground frame.

Why Necessary?

The same object can be at rest in one frame and in motion in another. Reference frame removes ambiguity.

2. Position Coordinate

Position coordinate tells the location of a particle on a chosen axis. In one-dimensional motion, position is written as x.

Origin

The point chosen as x = 0.

Positive Direction

Usually right side of origin is positive, but it must be defined in the problem.

Negative Direction

Opposite to chosen positive direction. Left side may be negative if right is positive.

Solved Example 1

Question: A particle is 5 m to the right of origin. Write its position coordinate.

Given: Right direction is positive.

Formula: x = + distance from origin

Calculation: x = +5 m

Final Answer: x = +5 m

Exam Tip: Always mention sign with position coordinate.

Solved Example 2

Question: A particle is 3 m to the left of origin. Write its position coordinate.

Given: Right positive, left negative.

Formula: x = - distance from origin

Calculation: x = -3 m

Final Answer: x = -3 m

Exam Tip: Coordinate depends on chosen positive direction.

3. Distance

Distance is the total length of the actual path travelled by an object. It is a scalar quantity and depends on the path followed.

Scalar Quantity

Distance has magnitude only, no direction.

Path Dependent

Different paths between same points may have different distances.

SI Unit

The SI unit of distance is metre, symbol m.

4. Displacement

Displacement is the shortest directed distance from initial position to final position. It is a vector quantity.

Positive Displacement

If final position is in positive direction from initial position, displacement is positive.

Negative Displacement

If final position is in negative direction from initial position, displacement is negative.

Zero Displacement

If initial and final positions are same, displacement is zero even if distance is non-zero.

Displacement = final position - initial position = x₂ - x₁

5. Distance vs Displacement

Point	Distance	Displacement
Definition	Total path length travelled.	Shortest directed change in position.
Nature	Scalar.	Vector.
Sign	Never negative.	Positive, negative or zero.
Dependence	Depends on path.	Depends only on initial and final positions.
Magnitude	Always greater than or equal to magnitude of displacement.	Magnitude never exceeds distance.
Example	Walk 3 m east then 3 m west: distance = 6 m.	Same walk: displacement = 0.

Important result: Distance ≥ |Displacement|.

6. Sign Convention

Sign convention means choosing one direction as positive and the opposite direction as negative. It makes one-dimensional vector calculations simple.

7. Graphical Understanding

Position Coordinate

On a number line, each point has a coordinate. Movement from x₁ to x₂ gives displacement x₂ - x₁.

Round Trip

Returning to start gives zero displacement but non-zero distance.

Positive and Negative Displacement

Sign depends on chosen positive axis, not on whether the object is speeding up or slowing down.

Graph-Based Meaning

In an x-t graph, vertical coordinate gives position. Change in position between two times gives displacement.

8. Solved Numericals

CBSE Numerical 1

Question: A student walks 4 m east and then 3 m west. Find distance and displacement.

Given: Path = 4 m east + 3 m west.

Formula: Distance = total path, displacement = final - initial.

Calculation: Distance = 4 + 3 = 7 m; displacement = +4 - 3 = +1 m.

Final Answer: Distance = 7 m, displacement = 1 m east.

Exam Tip: Draw a number line for opposite directions.

NEET Numerical 1

Question: A body moves from x = -2 m to x = +5 m. Find displacement and distance if path is straight.

Given: x₁ = -2 m, x₂ = +5 m.

Formula: Displacement = x₂ - x₁.

Calculation: Displacement = 5 - (-2) = 7 m; straight distance = 7 m.

Final Answer: 7 m, 7 m.

Exam Tip: On straight path without reversal, distance equals displacement magnitude.

JEE Main Numerical 1

Question: A particle moves from x = 0 to x = 8 m, then to x = 2 m. Find distance and displacement.

Given: 0 → 8 → 2.

Formula: Distance = sum of path lengths; displacement = final - initial.

Calculation: Distance = 8 + 6 = 14 m; displacement = 2 - 0 = +2 m.

Final Answer: Distance = 14 m, displacement = +2 m.

Exam Tip: Distance counts reversals.

JEE Advanced Conceptual

Question: Can distance be zero while displacement is non-zero? Explain.

Given: Distance is total path length.

Formula: If no path is travelled, no position change occurs.

Calculation: Distance = 0 means object did not move, so displacement = 0.

Final Answer: No.

Exam Tip: Distance is always at least magnitude of displacement.

IB Numerical

Question: A runner completes one circular lap of radius 50 m. Find distance and displacement.

Given: One complete circle, r = 50 m.

Formula: Distance = circumference, displacement = 0.

Calculation: Distance = 2πr = 100π m ≈ 314 m; displacement = 0.

Final Answer: Distance ≈ 314 m, displacement = 0.

Exam Tip: Complete round trip gives zero displacement.

IGCSE Numerical

Question: A car travels 120 m north and then 50 m south. Find total distance and displacement.

Given: North positive.

Formula: Distance = 120 + 50; displacement = 120 - 50.

Calculation: Distance = 170 m; displacement = 70 m north.

Final Answer: 170 m, 70 m north.

Exam Tip: Opposite directions subtract for displacement.

A-Level Numerical

Question: A particle starts at x = 6 m and ends at x = -4 m after travelling through x = 10 m. Find displacement.

Given: x₁ = 6 m, x₂ = -4 m.

Formula: Displacement = x₂ - x₁.

Calculation: -4 - 6 = -10 m.

Final Answer: -10 m.

Exam Tip: Intermediate path is irrelevant for displacement.

CBSE Numerical 2

Question: A boy walks 5 m east, 5 m north and returns to starting point. Find displacement.

Given: Initial point = final point.

Formula: Displacement = final position - initial position.

Calculation: Since final and initial positions are same, displacement = 0.

Final Answer: 0.

Exam Tip: Closed path gives zero displacement.

9. PYQ Section and 60-Question Bank

Authentic year is used only when certain; otherwise questions are marked exam-style to avoid fake year labels.

CBSE Exam-style Question 1

Question: Reference frame is required because

(a) motion is relative(b) motion is always absolute(c) distance is vector(d) time stops

Correct Answer: motion is relative

Solution: Motion/rest depends on observer.

Exam Tip: Always identify observer.

NEET Exam-style Question 2

Question: Distance is a

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

Correct Answer: scalar

Solution: Distance has magnitude only.

Exam Tip: Distance has no direction.

JEE Main Exam-style Question 3

Question: Displacement is

(a) vector(b) scalar(c) always positive(d) path length

Correct Answer: vector

Solution: It has magnitude and direction/sign.

Exam Tip: Displacement depends on initial and final positions.

JEE Advanced Exam-style Question 4

Question: For round trip, displacement is

(a) zero(b) equal to distance(c) negative always(d) infinite

Correct Answer: zero

Solution: Final position equals initial position.

Exam Tip: Closed path means zero displacement.

IB Exam-style Question 5

Question: Distance compared with displacement magnitude is always

(a) greater or equal(b) less(c) equal only(d) negative

Correct Answer: greater or equal

Solution: Shortest path cannot exceed actual path.

Exam Tip: Use distance ≥ |displacement|.

IGCSE Exam-style Question 6

Question: A particle moves from x = 2 m to x = -3 m. Displacement is

(a) -5 m(b) +5 m(c) 1 m(d) -1 m

Correct Answer: -5 m

Solution: x₂ - x₁ = -3 - 2 = -5 m.

Exam Tip: Keep signs carefully.

A-Level Exam-style Question 7

Question: If right is positive, left movement gives

(a) negative displacement(b) positive displacement(c) zero distance(d) negative distance

Correct Answer: negative displacement

Solution: Left is opposite chosen positive direction.

Exam Tip: Distance is not negative.

CBSE Exam-style Question 8

Question: Distance depends on

(a) path(b) only final position(c) only initial position(d) mass

Correct Answer: path

Solution: Distance is total path length.

Exam Tip: Displacement ignores path.

NEET Exam-style Question 9

Question: Position coordinate is measured from

(a) origin(b) speedometer(c) mass centre only(d) clock

Correct Answer: origin

Solution: Coordinate requires chosen origin.

Exam Tip: Set origin first.

JEE Main Exam-style Question 10

Question: A body goes 3 m east and 4 m east. Distance and displacement are

(a) 7 m, 7 m east(b) 1 m, 7 m(c) 7 m, 1 m(d) 0, 7 m

Correct Answer: 7 m, 7 m east

Solution: Same direction, total path equals net change.

Exam Tip: No reversal means equality.

JEE Advanced Exam-style Question 11

Question: Reference frame is required because

(a) motion is relative(b) motion is always absolute(c) distance is vector(d) time stops

Correct Answer: motion is relative

Solution: Motion/rest depends on observer.

Exam Tip: Always identify observer.

IB Exam-style Question 12

Question: Distance is a

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

Correct Answer: scalar

Solution: Distance has magnitude only.

Exam Tip: Distance has no direction.

IGCSE Exam-style Question 13

Question: Displacement is

(a) vector(b) scalar(c) always positive(d) path length

Correct Answer: vector

Solution: It has magnitude and direction/sign.

Exam Tip: Displacement depends on initial and final positions.

A-Level Exam-style Question 14

Question: For round trip, displacement is

(a) zero(b) equal to distance(c) negative always(d) infinite

Correct Answer: zero

Solution: Final position equals initial position.

Exam Tip: Closed path means zero displacement.

CBSE Exam-style Question 15

Question: Distance compared with displacement magnitude is always

(a) greater or equal(b) less(c) equal only(d) negative

Correct Answer: greater or equal

Solution: Shortest path cannot exceed actual path.

Exam Tip: Use distance ≥ |displacement|.

NEET Exam-style Question 16

Question: A particle moves from x = 2 m to x = -3 m. Displacement is

(a) -5 m(b) +5 m(c) 1 m(d) -1 m

Correct Answer: -5 m

Solution: x₂ - x₁ = -3 - 2 = -5 m.

Exam Tip: Keep signs carefully.

JEE Main Exam-style Question 17

Question: If right is positive, left movement gives

(a) negative displacement(b) positive displacement(c) zero distance(d) negative distance

Correct Answer: negative displacement

Solution: Left is opposite chosen positive direction.

Exam Tip: Distance is not negative.

JEE Advanced Exam-style Question 18

Question: Distance depends on

(a) path(b) only final position(c) only initial position(d) mass

Correct Answer: path

Solution: Distance is total path length.

Exam Tip: Displacement ignores path.

IB Exam-style Question 19

Question: Position coordinate is measured from

(a) origin(b) speedometer(c) mass centre only(d) clock

Correct Answer: origin

Solution: Coordinate requires chosen origin.

Exam Tip: Set origin first.

IGCSE Exam-style Question 20

Question: A body goes 3 m east and 4 m east. Distance and displacement are

(a) 7 m, 7 m east(b) 1 m, 7 m(c) 7 m, 1 m(d) 0, 7 m

Correct Answer: 7 m, 7 m east

Solution: Same direction, total path equals net change.

Exam Tip: No reversal means equality.

A-Level Exam-style Question 21

Question: Reference frame is required because

(a) motion is relative(b) motion is always absolute(c) distance is vector(d) time stops

Correct Answer: motion is relative

Solution: Motion/rest depends on observer.

Exam Tip: Always identify observer.

CBSE Exam-style Question 22

Question: Distance is a

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

Correct Answer: scalar

Solution: Distance has magnitude only.

Exam Tip: Distance has no direction.

NEET Exam-style Question 23

Question: Displacement is

(a) vector(b) scalar(c) always positive(d) path length

Correct Answer: vector

Solution: It has magnitude and direction/sign.

Exam Tip: Displacement depends on initial and final positions.

JEE Main Exam-style Question 24

Question: For round trip, displacement is

(a) zero(b) equal to distance(c) negative always(d) infinite

Correct Answer: zero

Solution: Final position equals initial position.

Exam Tip: Closed path means zero displacement.

JEE Advanced Exam-style Question 25

Question: Distance compared with displacement magnitude is always

(a) greater or equal(b) less(c) equal only(d) negative

Correct Answer: greater or equal

Solution: Shortest path cannot exceed actual path.

Exam Tip: Use distance ≥ |displacement|.

IB Exam-style Question 26

Question: A particle moves from x = 2 m to x = -3 m. Displacement is

(a) -5 m(b) +5 m(c) 1 m(d) -1 m

Correct Answer: -5 m

Solution: x₂ - x₁ = -3 - 2 = -5 m.

Exam Tip: Keep signs carefully.

IGCSE Exam-style Question 27

Question: If right is positive, left movement gives

(a) negative displacement(b) positive displacement(c) zero distance(d) negative distance

Correct Answer: negative displacement

Solution: Left is opposite chosen positive direction.

Exam Tip: Distance is not negative.

A-Level Exam-style Question 28

Question: Distance depends on

(a) path(b) only final position(c) only initial position(d) mass

Correct Answer: path

Solution: Distance is total path length.

Exam Tip: Displacement ignores path.

CBSE Exam-style Question 29

Question: Position coordinate is measured from

(a) origin(b) speedometer(c) mass centre only(d) clock

Correct Answer: origin

Solution: Coordinate requires chosen origin.

Exam Tip: Set origin first.

NEET Exam-style Question 30

Question: A body goes 3 m east and 4 m east. Distance and displacement are

(a) 7 m, 7 m east(b) 1 m, 7 m(c) 7 m, 1 m(d) 0, 7 m

Correct Answer: 7 m, 7 m east

Solution: Same direction, total path equals net change.

Exam Tip: No reversal means equality.

JEE Main Exam-style Question 31

Question: Reference frame is required because

(a) motion is relative(b) motion is always absolute(c) distance is vector(d) time stops

Correct Answer: motion is relative

Solution: Motion/rest depends on observer.

Exam Tip: Always identify observer.

JEE Advanced Exam-style Question 32

Question: Distance is a

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

Correct Answer: scalar

Solution: Distance has magnitude only.

Exam Tip: Distance has no direction.

IB Exam-style Question 33

Question: Displacement is

(a) vector(b) scalar(c) always positive(d) path length

Correct Answer: vector

Solution: It has magnitude and direction/sign.

Exam Tip: Displacement depends on initial and final positions.

IGCSE Exam-style Question 34

Question: For round trip, displacement is

(a) zero(b) equal to distance(c) negative always(d) infinite

Correct Answer: zero

Solution: Final position equals initial position.

Exam Tip: Closed path means zero displacement.

A-Level Exam-style Question 35

Question: Distance compared with displacement magnitude is always

(a) greater or equal(b) less(c) equal only(d) negative

Correct Answer: greater or equal

Solution: Shortest path cannot exceed actual path.

Exam Tip: Use distance ≥ |displacement|.

CBSE Exam-style Question 36

Question: A particle moves from x = 2 m to x = -3 m. Displacement is

(a) -5 m(b) +5 m(c) 1 m(d) -1 m

Correct Answer: -5 m

Solution: x₂ - x₁ = -3 - 2 = -5 m.

Exam Tip: Keep signs carefully.

NEET Exam-style Question 37

Question: If right is positive, left movement gives

(a) negative displacement(b) positive displacement(c) zero distance(d) negative distance

Correct Answer: negative displacement

Solution: Left is opposite chosen positive direction.

Exam Tip: Distance is not negative.

JEE Main Exam-style Question 38

Question: Distance depends on

(a) path(b) only final position(c) only initial position(d) mass

Correct Answer: path

Solution: Distance is total path length.

Exam Tip: Displacement ignores path.

JEE Advanced Exam-style Question 39

Question: Position coordinate is measured from

(a) origin(b) speedometer(c) mass centre only(d) clock

Correct Answer: origin

Solution: Coordinate requires chosen origin.

Exam Tip: Set origin first.

IB Exam-style Question 40

Question: A body goes 3 m east and 4 m east. Distance and displacement are

(a) 7 m, 7 m east(b) 1 m, 7 m(c) 7 m, 1 m(d) 0, 7 m

Correct Answer: 7 m, 7 m east

Solution: Same direction, total path equals net change.

Exam Tip: No reversal means equality.

IGCSE Exam-style Question 41

Question: Reference frame is required because

(a) motion is relative(b) motion is always absolute(c) distance is vector(d) time stops

Correct Answer: motion is relative

Solution: Motion/rest depends on observer.

Exam Tip: Always identify observer.

A-Level Exam-style Question 42

Question: Distance is a

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

Correct Answer: scalar

Solution: Distance has magnitude only.

Exam Tip: Distance has no direction.

CBSE Exam-style Question 43

Question: Displacement is

(a) vector(b) scalar(c) always positive(d) path length

Correct Answer: vector

Solution: It has magnitude and direction/sign.

Exam Tip: Displacement depends on initial and final positions.

NEET Exam-style Question 44

Question: For round trip, displacement is

(a) zero(b) equal to distance(c) negative always(d) infinite

Correct Answer: zero

Solution: Final position equals initial position.

Exam Tip: Closed path means zero displacement.

JEE Main Exam-style Question 45

Question: Distance compared with displacement magnitude is always

(a) greater or equal(b) less(c) equal only(d) negative

Correct Answer: greater or equal

Solution: Shortest path cannot exceed actual path.

Exam Tip: Use distance ≥ |displacement|.

JEE Advanced Exam-style Question 46

Question: A particle moves from x = 2 m to x = -3 m. Displacement is

(a) -5 m(b) +5 m(c) 1 m(d) -1 m

Correct Answer: -5 m

Solution: x₂ - x₁ = -3 - 2 = -5 m.

Exam Tip: Keep signs carefully.

IB Exam-style Question 47

Question: If right is positive, left movement gives

(a) negative displacement(b) positive displacement(c) zero distance(d) negative distance

Correct Answer: negative displacement

Solution: Left is opposite chosen positive direction.

Exam Tip: Distance is not negative.

IGCSE Exam-style Question 48

Question: Distance depends on

(a) path(b) only final position(c) only initial position(d) mass

Correct Answer: path

Solution: Distance is total path length.

Exam Tip: Displacement ignores path.

A-Level Exam-style Question 49

Question: Position coordinate is measured from

(a) origin(b) speedometer(c) mass centre only(d) clock

Correct Answer: origin

Solution: Coordinate requires chosen origin.

Exam Tip: Set origin first.

CBSE Exam-style Question 50

Question: A body goes 3 m east and 4 m east. Distance and displacement are

(a) 7 m, 7 m east(b) 1 m, 7 m(c) 7 m, 1 m(d) 0, 7 m

Correct Answer: 7 m, 7 m east

Solution: Same direction, total path equals net change.

Exam Tip: No reversal means equality.

NEET Exam-style Question 51

Question: Reference frame is required because

(a) motion is relative(b) motion is always absolute(c) distance is vector(d) time stops

Correct Answer: motion is relative

Solution: Motion/rest depends on observer.

Exam Tip: Always identify observer.

JEE Main Exam-style Question 52

Question: Distance is a

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

Correct Answer: scalar

Solution: Distance has magnitude only.

Exam Tip: Distance has no direction.

JEE Advanced Exam-style Question 53

Question: Displacement is

(a) vector(b) scalar(c) always positive(d) path length

Correct Answer: vector

Solution: It has magnitude and direction/sign.

Exam Tip: Displacement depends on initial and final positions.

IB Exam-style Question 54

Question: For round trip, displacement is

(a) zero(b) equal to distance(c) negative always(d) infinite

Correct Answer: zero

Solution: Final position equals initial position.

Exam Tip: Closed path means zero displacement.

IGCSE Exam-style Question 55

Question: Distance compared with displacement magnitude is always

(a) greater or equal(b) less(c) equal only(d) negative

Correct Answer: greater or equal

Solution: Shortest path cannot exceed actual path.

Exam Tip: Use distance ≥ |displacement|.

A-Level Exam-style Question 56

Question: A particle moves from x = 2 m to x = -3 m. Displacement is

(a) -5 m(b) +5 m(c) 1 m(d) -1 m

Correct Answer: -5 m

Solution: x₂ - x₁ = -3 - 2 = -5 m.

Exam Tip: Keep signs carefully.

CBSE Exam-style Question 57

Question: If right is positive, left movement gives

(a) negative displacement(b) positive displacement(c) zero distance(d) negative distance

Correct Answer: negative displacement

Solution: Left is opposite chosen positive direction.

Exam Tip: Distance is not negative.

NEET Exam-style Question 58

Question: Distance depends on

(a) path(b) only final position(c) only initial position(d) mass

Correct Answer: path

Solution: Distance is total path length.

Exam Tip: Displacement ignores path.

JEE Main Exam-style Question 59

Question: Position coordinate is measured from

(a) origin(b) speedometer(c) mass centre only(d) clock

Correct Answer: origin

Solution: Coordinate requires chosen origin.

Exam Tip: Set origin first.

JEE Advanced Exam-style Question 60

Question: A body goes 3 m east and 4 m east. Distance and displacement are

(a) 7 m, 7 m east(b) 1 m, 7 m(c) 7 m, 1 m(d) 0, 7 m

Correct Answer: 7 m, 7 m east

Assertion: Zero displacement can occur with non-zero distance.

Reason: A body may return to starting point.

Answer: (a)

Explanation: Correct.

11. Case Study Questions

Case Study: Train Motion

A passenger sitting in a moving train sees another passenger at rest, while a person standing on the platform sees both passengers moving.

Questions: Which frame sees passenger at rest?; Which frame sees passenger moving?; What concept is shown?; Why is reference frame important?

Answers: Train frame; platform frame; relativity of motion; same object may have different motion descriptions.

Explanation: The case highlights reference frame, path length and vector displacement in everyday motion.

Case Study: Car Motion

A car travels 100 m east, then 40 m west on a straight road.

Questions: Find distance; find displacement; is distance scalar?; can displacement be negative?

Answers: 140 m; 60 m east; yes; yes depending on direction.

Explanation: The case highlights reference frame, path length and vector displacement in everyday motion.

Case Study: Circular Track Motion

A runner completes one full lap of a circular track.

Questions: What is displacement?; What is distance?; Why are they different?; What if half lap is completed?

Answers: Zero; circumference; path length non-zero but final position same; displacement equals diameter in magnitude.

Explanation: The case highlights reference frame, path length and vector displacement in everyday motion.

Case Study: Walking Path

A student walks 3 m north, 4 m east and stops.

Questions: What is distance?; What is displacement magnitude?; Which is scalar?; Which has direction?

Answers: 7 m; 5 m; distance; displacement.

Explanation: The case highlights reference frame, path length and vector displacement in everyday motion.

Case Study: Round-trip Journey

A bus goes from city A to city B and returns to A.

Questions: What is final displacement?; Is distance zero?; Why?; Which quantity depends on path?

Answers: Zero; no; bus travelled a path; distance.

Explanation: The case highlights reference frame, path length and vector displacement in everyday motion.

12. Quick Revision Notes

One-page Revision Sheet

Reference frame is needed to describe motion.
Position coordinate is measured from origin.
Distance is total path length.
Displacement = x₂ - x₁.

Common Mistakes

Writing distance as negative.
Ignoring sign convention.
Confusing path length with shortest path.
Forgetting zero displacement in round trip.

Exam Tips

Draw number line for 1D questions.
Mark initial and final positions.
Use distance ≥ |displacement|.
Use signs only for vector quantities.

Most important concepts: reference frame, origin, sign convention, scalar vs vector nature, distance vs displacement and round-trip motion.

Searching for a Physics Tutor?

For CBSE, NEET, JEE Main, JEE Advanced, IB, IGCSE and A-Level Physics, contact Kumar Sir for one-to-one online Physics classes.

Phone: +91-9958461445Email: kumarsirphysics@gmail.com Website: https://kumarphysicsclasses.com WhatsApp Kumar Sir