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Class 9 Science – Chapter: Motion 

✨ Introduction to Motion

• A body is said to be in motion if it changes its position with respect to time.

• If it does not change its position, it is said to be at rest.

Example: A book on a table is at rest, while a car moving on a road is in motion.

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🔹 Types of Motion

Type of Motion	Description	Example
Translatory Motion	Moves from one point to another	Car moving on a road
Rotatory Motion	Motion around a fixed axis	Fan blades
Oscillatory Motion	To and fro motion about a mean position	Pendulum
Periodic Motion	Repeats after fixed time intervals	Motion of Earth around Sun
Random Motion	Irregular, unpredictable motion	Movement of gas molecules

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🔹 Distance and Displacement

• Distance: Total path covered by a body (scalar quantity).

• Displacement: Shortest distance between initial and final position (vector quantity).

Quantity	Type	Can be Zero?	Direction?
Distance	Scalar	No	No
Displacement	Vector	Yes	Yes (with sign)

Example: If you walk 4 m east and then 3 m west, total distance = 7 m; displacement = 1 m east.

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🔹 Speed and Velocity

• Speed = Distance / Time (scalar)

• Velocity = Displacement / Time (vector)

Quantity	Formula	Unit	Type
Speed	Distance ÷ Time	m/s	Scalar
Velocity	Displacement ÷ Time	m/s	Vector

Types of Speed:

• Uniform Speed: Constant speed

• Non-uniform Speed: Changing speed

• Average Speed = Total Distance ÷ Total Time

• Instantaneous Speed: Speed at a particular moment

Example: If a car travels 100 km in 2 hours, speed = 100 ÷ 2 = 50 km/h

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🔹 Acceleration

• The rate of change of velocity with time.

Acceleration (a) = (Final Velocity – Initial Velocity) ÷ Time

• a = (v – u) ÷ t

Where:

• u = initial velocity

• v = final velocity

• t = time taken

• a = acceleration

Case	Description	Acceleration Sign
Increasing speed	Velocity increases	Positive
Decreasing speed	Velocity decreases (retardation)	Negative

Example: A bike speeds up from 10 m/s to 30 m/s in 5 seconds.
a = (30 – 10) ÷ 5 = 4 m/s²

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🔹 Graphical Representation of Motion

1. Distance-Time Graph

• Slope gives speed.

• Straight line = uniform speed

• Curved line = non-uniform speed

Distance (y-axis)
^
|        *
|     *
|  *
|____________________> Time (x-axis)

Example: A straight line in distance-time graph indicates a car moving at uniform speed.

2. Velocity-Time Graph

• Slope = Acceleration

• Area under graph = Displacement

Graph Type	Physical Meaning
Straight line (positive slope)	Uniform acceleration
Horizontal line	Uniform velocity
Straight line (negative slope)	Retardation

Velocity-Time Graph Example (Uniform Acceleration):

Velocity (y-axis)
^
|         /
|       /
|     /
|   /
|____________________> Time (x-axis)

Example: An object accelerating uniformly from rest will have a straight, upward-sloping line.

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🔹 Equations of Uniformly Accelerated Motion

1. v = u + at

2. s = ut + (1/2)at²

3. v² = u² + 2as

Where:

• s = displacement

• u = initial velocity

• v = final velocity

• a = acceleration

• t = time

Derivation available on request.

Example: A scooter starts from rest (u = 0) and accelerates at 2 m/s² for 3 seconds. Find v and s:

• v = 0 + 2×3 = 6 m/s

• s = 0 + (1/2)×2×9 = 9 m

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📚 Uniform and Non-Uniform Motion

Type	Definition	Example
Uniform Motion	Equal distance in equal time intervals	Car on highway
Non-uniform Motion	Unequal distance in equal time intervals	Traffic in city roads

Example: A train moving at 60 km/h throughout is in uniform motion, but a bus in traffic is in non-uniform motion.

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🎯 Numerical Example

A car starts from rest and accelerates at 4 m/s² for 5 seconds. Find the final velocity and distance covered.

Given: u = 0, a = 4 m/s², t = 5 s

• Final velocity: v = u + at = 0 + 4 × 5 = 20 m/s

• Distance: s = ut + (1/2)at² = 0 + (1/2) × 4 × 25 = 50 m

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