Chapter 2 — Understanding Motion through Experience

1. What is motion?

An object is in motion when its position changes with time relative to a chosen reference point.

Thus, motion is relative.

A person sitting inside a moving train may be at rest relative to another passenger but moving relative to an observer standing on the platform.

2. Frame of reference

A reference point or frame is necessary to describe motion.

The chapter distinguishes:

• Inertial frame: at rest or moving with constant velocity; Newton’s laws apply without modification.
• Non-inertial frame: accelerating frame; apparent or pseudo forces may need to be considered.

3. Scalars and vectors

Scalar: has magnitude only.

Examples:

• distance
• time
• mass
• speed
• work

Vector: has magnitude and direction.

Examples:

• displacement
• velocity
• force

This distinction is fundamental because direction can change the result even when the magnitude remains the same.

4. Distance and displacement

Distance is the total path travelled and is a scalar.

Displacement describes the change from the initial position to the final position and has direction.

If a student walks from A to B and then returns to A:

• distance is not zero;
• displacement is zero.

5. Vector addition

Vectors can be combined graphically using methods such as:

• triangle method
• parallelogram method

For example, a displacement of 4 units east followed by 3 units north gives a resultant displacement represented by the line joining the initial and final points.

6. Equations of motion

For uniformly accelerated motion:$$v=u+at$$$$s=ut+\frac12at^2$$$$v^2=u^2+2as$$

where:

• $u$ = initial velocity
• $v$ = final velocity
• $a$ = acceleration
• $t$ = time
• $s$ = displacement

The chapter also derives the distance travelled during the nth second:$$s_n=u+\frac{a}{2}(2n-1)$$

This represents the distance covered during that particular one-second interval, not the total distance from the beginning.

Key idea

Before solving any motion problem, identify the reference frame, the direction, and whether the quantity is scalar or vector.

Chapter 2 — Understanding Motion through Experience

Questions

A. Multiple Choice Questions

1. The state of motion of an object is described relative to a:
a) Mass
b) Reference frame
c) Force
d) Unit

2. Which of the following is a vector quantity?
a) Distance
b) Speed
c) Mass
d) Displacement

3. Which quantity has magnitude but no direction?
a) Velocity
b) Acceleration
c) Distance
d) Displacement

4. A passenger sitting in a moving train is at rest relative to:
a) A tree beside the railway track
b) The road
c) Another passenger moving with the train
d) A person standing on the platform

5. If an object returns to its starting point, its displacement is:
a) Equal to the distance
b) Maximum
c) Zero
d) Always negative

6. The equation $v=u+at$ applies to:
a) Uniformly accelerated motion
b) Only circular motion
c) Random motion
d) Static objects

7. The displacement during the $n^{th}$ second is represented by:
a) $u+an$
b) $u+\frac a2(2n-1)$
c) $ut$
d) $v^2-u^2$

B. Fill in the Blanks

8. Motion is described relative to a ______ of reference.

9. Velocity is a ______ quantity.

10. Speed is a ______ quantity.

11. An accelerating reference frame is called a ______-inertial frame.

12. The SI unit of acceleration is ______.

C. True or False

13. Distance has a direction.

14. Displacement can be zero even when distance travelled is not zero.

15. A vector quantity requires magnitude and direction.

16. Motion is always described identically by all observers.

D. Short Answer Questions

17. Why is motion called relative?

18. Distinguish between distance and displacement.

19. Why is displacement useful when direction of motion is important?

20. Give two examples of vector quantities encountered in everyday life.

E. Numerical Questions

21. A body starts from rest and accelerates uniformly at $4\,m/s^2$. Find the distance travelled during the 6th second.

22. A car has an initial velocity of $8\,m/s$ and accelerates at $2\,m/s^2$. Find the distance covered during the 5th second.

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Answers

A. MCQ Answers

1. b) Reference frame
2. d) Displacement
3. c) Distance
4. c) Another passenger moving with the train
5. c) Zero
6. a) Uniformly accelerated motion
7. b) u+a2(2n−1)u+\frac a2(2n-1)

B. Fill in the Blanks

8. frame
9. vector
10. scalar
11. non
12. m/s2m/s^2

C. True/False

13. False
14. True
15. True
16. False

D. Answers

17. Motion is relative because the description of an object’s motion depends on the reference frame of the observer.
18. Distance is the total length of the path travelled and is a scalar. Displacement is the change in position from the initial to the final point and is a vector.
19. Displacement includes direction as well as magnitude, whereas distance does not.
20. Velocity and displacement.

E. Numerical Answers

$$s_n=u+\frac a2(2n-1)$$

Given $u=0,\ a=4,\ n=6$:$$s_6=0+\frac42(12-1)$$$$\boxed{22m}$$

$$s_5=u+\frac a2(2n-1)$$$$=8+\frac22(10-1)$$$$=8+9$$$$\boxed{17m}$$

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