Motion — Class 9 Physical Science

"Everything in the universe MOVES. The Earth around the Sun. The car on the road. The blood in your veins. Understanding motion is understanding the physical world."

1. About the Chapter

Motion is the CHANGE in position of an object with respect to TIME and a REFERENCE POINT. This chapter covers:

• Distance vs Displacement — the crucial distinction between scalars and vectors
• Speed vs Velocity — average and instantaneous
• Acceleration — the rate of change of velocity
• Three Equations of Motion — for uniform acceleration
• Graphs of Motion — distance-time and velocity-time
• Uniform Circular Motion — speed constant, velocity changing

Why This Chapter Matters

• Motion is the FOUNDATION of all of physics — from mechanics to quantum theory
• Understanding velocity-time graphs is ESSENTIAL for all higher physics
• The equations of motion are used in engineering, sports science, and everyday life

2. Rest and Motion — The Reference Point

An object is at REST if its position does NOT change with time (relative to a reference point). An object is in MOTION if its position CHANGES with time. 'Motion is RELATIVE. A passenger sitting in a moving train is at rest relative to the train — but in motion relative to the ground.'

3. Distance vs Displacement

Example — The Critical Difference

'A person walks 3 km EAST, then 4 km NORTH. Distance travelled = 3 + 4 = 7 km. Displacement = √(3² + 4²) = 5 km (direction: Northeast, at an angle tan⁻¹(4/3) ≈ 53° from East).'

'If the person walks in a CIRCLE of radius r and returns to the starting point: Distance = 2πr (the circumference). Displacement = 0 (start and end are the SAME point).'

4. Speed and Velocity

Speed (Scalar)

Speed = Distance / Time

• Average Speed = Total distance / Total time
• Instantaneous Speed = Speed at a SPECIFIC instant (shown by speedometer of a vehicle)
• Unit: m/s or km/h. 1 km/h = 5/18 m/s.

Velocity (Vector)

Velocity = Displacement / Time

• Average Velocity = Total displacement / Total time
• Unit: m/s, WITH DIRECTION.

Uniform vs Non-Uniform Motion

Uniform: Equal distances in EQUAL time intervals. Speed is CONSTANT. Non-Uniform: Unequal distances in equal time intervals. Speed VARIES.

5. Acceleration

Acceleration (a) = Change in velocity / Time taken = (v − u) / t

• Unit: m/s²
• Positive acceleration: velocity INCREASES (speeding up)
• Negative acceleration (Retardation/Deceleration) : velocity DECREASES (slowing down)
• Zero acceleration: velocity CONSTANT (uniform motion)

Example

'A car starts from rest (u = 0) and reaches 20 m/s in 10 seconds. Acceleration = (20 − 0)/10 = 2 m/s². Every second, the car's velocity increases by 2 m/s.'

6. Three Equations of Motion (Uniform Acceleration)

These apply ONLY when acceleration is CONSTANT.

u = initial velocity (m/s). v = final velocity (m/s). a = acceleration (m/s²). t = time (s). s = displacement (m).

Worked Example 1

'A car accelerates uniformly from 18 km/h to 36 km/h in 5 seconds. Find (i) acceleration, (ii) distance covered.'

Step 1 — Convert to m/s: u = 18 × 5/18 = 5 m/s. v = 36 × 5/18 = 10 m/s. Step 2 — Acceleration: a = (v−u)/t = (10−5)/5 = 1 m/s². Step 3 — Distance: s = ut + ½at² = (5×5) + ½(1)(25) = 25 + 12.5 = 37.5 m.

Worked Example 2

'A ball is thrown vertically upward with a velocity of 20 m/s. How high does it go? (g = 10 m/s²)'

At the HIGHEST POINT: v = 0. u = 20 m/s. a = −g = −10 m/s² (against gravity). Using v² = u² + 2as: 0 = 400 + 2(−10)s → 20s = 400 → s = 20 m.

7. Graphs of Motion

Distance-Time Graph

• Slope = SPEED. Steeper slope = faster speed. Straight line = uniform speed. Curved line = changing speed (acceleration). Horizontal line = AT REST.

Velocity-Time Graph

• Slope = ACCELERATION. AREA under the graph = DISPLACEMENT. Straight rising line = uniform acceleration. Straight horizontal line = uniform velocity. Straight falling line = uniform retardation.

Worked Example — Reading a v-t Graph

'A car's velocity-time graph shows: 0 to 10s: velocity increases from 0 to 20 m/s (straight line). 10s to 20s: constant 20 m/s. 20s to 30s: velocity decreases from 20 to 0 m/s (straight line). Find (i) acceleration during first 10s, (ii) retardation during last 10s, (iii) total distance travelled.'

(i) a = (20−0)/10 = 2 m/s². (ii) a = (0−20)/10 = −2 m/s² (retardation). (iii) Distance = Area under v-t graph = area of trapezoid 1 + rectangle + trapezoid 2.

8. Uniform Circular Motion

When an object moves in a CIRCULAR PATH at CONSTANT SPEED: speed is constant. Velocity CHANGES (direction continuously changes → acceleration exists). This acceleration is called CENTRIPETAL ACCELERATION — directed toward the CENTRE of the circle.

a_c = v²/r (v = speed, r = radius of circle). Examples: Moon orbiting Earth. A stone tied to a string, whirled around. A car taking a circular turn.

'The force providing centripetal acceleration is the CENTRIPETAL FORCE. If this force disappears (e.g., string breaks) → the object flies off TANGENTIALLY — NOT radially outward.'

9. Common Mistakes to Avoid

1. 'Distance and displacement are the same' — Distance is the PATH. Displacement is the SHORTEST STRAIGHT LINE. After a 400m lap on a track: distance = 400m, displacement = 0.
2. 'Velocity and speed are the same' — Speed is |velocity| (magnitude). Velocity tells DIRECTION too. Constant speed in a circle = CONSTANTLY CHANGING velocity.
3. 'Acceleration always means speeding up' — Acceleration is ANY change in velocity — speeding up, slowing down (retardation), OR changing direction (circular motion).
4. Using km/h directly in equations of motion — ALWAYS convert to m/s first. 1 km/h = 5/18 m/s.
5. Forgetting the sign of 'g' — When an object is thrown UP: a = −g (velocity decreases). When it falls DOWN: a = +g.

10. AP SSC Exam Focus

Key Tip

'In numerical problems: List ALL given values with proper units. Write the equation. Substitute. Solve. Check units. The quadratic equation s = ut + ½at² often yields TWO solutions for t — select the PHYSICALLY MEANINGFUL one.'