Class 9 Science Chapter 4 | Describing Motion Around Us

1. What Is Motion?

Everything in nature is in motion in some way — from planets and galaxies to dust particles, animals and molecules.

Motion is studied by first simplifying complicated real-world motion into idealised forms. This chapter focuses on motion in a straight line and uniform circular motion.

📍 PositionWhere an object is located relative to a chosen reference point.

↔️ DistanceTotal length of the path travelled.

🧭 DisplacementChange in position with direction.

🏃 SpeedHow fast distance is covered.

➡️ VelocityRate of change of displacement.

⚡ AccelerationRate of change of velocity.

Chapter goal: describe motion not only in words, but also using numbers, equations and graphs.

2. Motion in a Straight Line — Describing Position

When an object moves along a straight path, its motion is called linear motion or motion in a straight line.

To describe position, choose a fixed reference point (origin) and a direction. On a straight line, positions on one side of the origin can be taken as positive and those on the other side as negative.

Choose reference point O

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Choose positive direction

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Assign position

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Track position with time

Rest and motion are relative

An object is in motion if its position changes with time relative to the chosen reference point. It is at rest if its position does not change relative to that reference point.

Example: A passenger sitting in a moving train is at rest relative to the train but in motion relative to the ground. Therefore, motion and rest depend on the reference frame.

3. Distance Travelled and Displacement

Distance

Distance is the total length of the actual path travelled by an object. It is a scalar quantity, so only magnitude is needed.

Displacement

Displacement is the change in position of an object from its initial position to its final position, along with direction. It is a vector quantity.

Distance	Displacement
Total path length.	Change in position from initial to final point.
Scalar.	Vector.
Never negative.	Can be positive, negative or zero in one-dimensional motion depending on chosen direction.
Depends on actual path.	Depends only on initial and final positions.
For a moving object, it is generally greater than or equal to displacement magnitude.	Magnitude is less than or equal to distance.

|Displacement| ≤ Distance

Example: Athlete returning to the start

If an athlete runs 100 m forward and then 60 m backward, the distance travelled is 160 m. The displacement magnitude is 40 m in the forward direction.

Exam alert: An object can travel a non-zero distance and still have zero displacement if it returns to its starting point.

4. Average Speed and Average Velocity

Average speed

Average speed = Total distance travelled ÷ Total time taken

Speed tells us how quickly distance is covered. It does not include direction.

Average velocity

Average velocity = Total displacement ÷ Total time taken

Velocity includes direction because displacement is a vector.

Quantity	Formula	Nature
Average speed	distance / time	Scalar
Average velocity	displacement / time	Vector

Uniform and non-uniform motion

In uniform motion in a straight line, an object covers equal distances in equal intervals of time. If it covers unequal distances in equal intervals, its motion is non-uniform.

India's scientific contribution: The NCERT chapter connects the distance–time–speed relationship with ancient Indian mathematical traditions, including Aryabhata's Aryabhatiya and a problem from the 14th-century Ganitakaumudi.

5. Average Acceleration

Acceleration measures how quickly velocity changes with time.

Average acceleration = Change in velocity ÷ Time interval = (v − u) / t

Here u is initial velocity, v is final velocity and t is the time interval.

Positive accelerationVelocity changes in the positive direction according to the chosen convention.

Negative accelerationVelocity changes in the negative direction; depending on the motion, this may represent slowing down.

Zero accelerationVelocity remains constant.

Important: Acceleration does not simply mean “speeding up”. An object can have acceleration whenever its velocity changes, including a change in direction.

6. Graphical Representation of Motion

Graphs can show how an object's position or velocity changes with time. They allow us to interpret motion visually and quantitatively.

Position–time graph

The slope of a position–time graph gives the velocity.

Straight sloping line: constant velocity. Horizontal line: object is at rest.

Velocity–time graph

The slope of a velocity–time graph gives acceleration. The area under a velocity–time graph represents displacement for the interval shown.

Graph	What its slope tells us	Other useful information
Position–time	Velocity	Position is read from the vertical axis.
Velocity–time	Acceleration	Area under graph gives displacement.

7. Kinematic Equations for Constant Acceleration

For straight-line motion with constant acceleration, three important equations connect displacement, velocity, acceleration and time.

v = u + at

s = ut + ½at²

v² = u² + 2as

Symbol	Meaning	SI unit
u	Initial velocity	m/s
v	Final velocity	m/s
a	Constant acceleration	m/s²
t	Time interval	s
s	Displacement	m

Condition: These standard equations are used for motion in a straight line when acceleration is constant.

How to solve a numerical

Read the problem

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List u, v, a, t, s

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Choose equation

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Substitute with units

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Check answer

8. Motion in a Plane — Uniform Circular Motion

When an object moves along a circular path, its direction changes continuously. In uniform circular motion, the speed remains constant but the direction of velocity changes continuously.

SpeedConstant in uniform circular motion.

VelocityChanges because its direction changes.

AccelerationPresent because velocity changes, and it is directed towards the centre of the circular path.

Centripetal acceleration: a_c = v²/r

Here v is speed and r is the radius of the circular path.

Examples

A satellite moving approximately in a circular orbit.
A stone whirled on a string.
A point on a rotating fan blade.
A car moving around a circular track at constant speed.

Most important concept: Constant speed does not mean zero acceleration if direction is changing. Uniform circular motion is therefore accelerated motion.

9. Formula Sheet

Concept	Formula
Average speed	distance / time
Average velocity	displacement / time
Average acceleration	(v − u) / t
First equation of motion	v = u + at
Second equation of motion	s = ut + ½at²
Third equation of motion	v² = u² + 2as
Uniform circular motion	a_c = v²/r

Units: distance/displacement → metre (m); time → second (s); speed/velocity → m/s; acceleration → m/s².

10. Quick Revision Capsule

MotionChange in position with time relative to a reference point.

DistanceTotal path length; scalar.

DisplacementChange in position with direction; vector.

SpeedDistance travelled per unit time.

VelocityDisplacement per unit time.

AccelerationChange in velocity per unit time.

Position–time slopeVelocity.

Velocity–time slopeAcceleration.

Velocity–time areaDisplacement.

Uniform circular motionConstant speed but changing velocity because direction changes.

Most important differences

Pair	Remember
Distance vs displacement	Actual path length vs change in position.
Speed vs velocity	Scalar rate of distance vs vector rate of displacement.
Uniform vs non-uniform motion	Equal distances in equal time intervals vs unequal distances in equal intervals.
Speed vs acceleration	Speed describes how fast distance is covered; acceleration describes change in velocity.
Constant speed vs constant velocity	Constant speed may still have changing direction; constant velocity requires both magnitude and direction to remain unchanged.

One-line summary: Motion is described precisely by tracking position and using distance, displacement, speed, velocity, acceleration, graphs and equations.

11. Practice Questions

Short Answer

What is meant by motion?
Why is a reference point required to describe motion?
Explain why rest and motion are relative.
Differentiate between distance and displacement.
Can displacement be zero when distance is not zero? Explain.
Define average speed and average velocity.
Differentiate between uniform and non-uniform motion.
What is acceleration?
What does the slope of a position-time graph represent?
What does the slope and area of a velocity-time graph represent?
Write the three equations of motion for constant acceleration.
Under what condition are the three kinematic equations applicable?
Why is uniform circular motion an accelerated motion even when speed is constant?
What is centripetal acceleration?
A car travels 120 m in 10 s. Calculate its average speed.

Answer Hints

1. Change in position with time relative to a reference point.
2. Position must be specified relative to something fixed.
3. The same object can be at rest relative to one reference frame and moving relative to another.
4. Distance is total path length; displacement is change in position with direction.
5. Yes. Returning to the starting point gives zero displacement but non-zero distance.
6. Average speed = total distance/total time; average velocity = total displacement/total time.
7. Equal distances in equal time intervals vs unequal distances in equal intervals.
8. Rate of change of velocity.
9. Velocity.
10. Slope = acceleration; area = displacement.
11. v = u + at; s = ut + ½at²; v² = u² + 2as.
12. Straight-line motion with constant acceleration.
13. Direction of velocity continuously changes, so velocity changes.
14. Acceleration directed towards the centre of a circular path; a_c = v²/r.
15. Average speed = 120/10 = 12 m/s.

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