Motion Class 9 Notes: Equations of Motion, Graphs and Solved Numericals

Motion is the first physics chapter of Class 9 Science and the base for Class 11 kinematics. These notes give the definitions, the three equations, graph rules and worked numericals in simple language.

Distance vs displacement

Distance is the total path length (scalar, never negative). Displacement is the shortest straight-line distance from start to end with direction (vector, can be zero). A runner completing one 400 m lap: distance 400 m, displacement 0.

Speed, velocity, acceleration

• Speed = distance/time (m/s). Velocity = displacement/time.
• Average speed = total distance / total time.
• Acceleration a = (v − u)/t, unit m/s². Negative acceleration = retardation.

The three equations of motion (uniform acceleration)

1. v = u + at
2. s = ut + ½at²
3. v² = u² + 2as

u = initial velocity, v = final velocity, a = acceleration, t = time, s = distance. Choose the equation that has the three known quantities and the one you want.

Graphs

Graph	Slope gives	Area gives
Distance–time	Speed	—
Velocity–time	Acceleration	Distance

Straight sloping line on a distance–time graph = uniform speed; curve = non-uniform. Horizontal line on a velocity–time graph = uniform velocity.

Solved numericals

1. A bus starts from rest and reaches 20 m/s in 10 s. Find acceleration and distance. a = (20 − 0)/10 = 2 m/s². s = 0 + ½ × 2 × 100 = 100 m.

2. A car moving at 30 m/s brakes with retardation 6 m/s². Stopping distance? v² = u² + 2as → 0 = 900 − 12s → s = 75 m.

3. A stone dropped from a tower reaches the ground in 3 s (g = 10 m/s²). Height = ½ × 10 × 9 = 45 m.

Uniform circular motion

Speed constant but direction changes, so velocity changes → accelerated motion. Speed v = 2πr/t.

Common mistakes

• Using km/h with metres: convert (÷ 3.6 for km/h → m/s).
• Forgetting u = 0 for “starts from rest” and v = 0 for “comes to rest”.
• Reading slope of a velocity–time graph as speed.

Continue to Laws of Motion (Class 11) once you finish this chapter.

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Frequently asked questions

Can displacement be greater than distance?

No. Displacement is always less than or equal to distance.

How do I decide which equation of motion to use?

List the known values and the unknown. Pick the equation that contains all of them and nothing else.

What does the area under a speed-time graph give?

The distance travelled.