Motion: Class 9 Study Guide
We describe motion using distance, speed and acceleration. The equations connect them.
Distance is the total length of the path travelled. Displacement is the shortest straight-line distance from start to end, with a direction. Speed is distance ÷ time. Velocity is displacement ÷ time. Acceleration is the rate of change of velocity: a = (v − u) ÷ t.
Speed is measured in m/s. To change km/h to m/s, multiply by 5/18.
Equations of motion
For constant acceleration a, with initial velocity u, final velocity v, time t and displacement s:
| Equation | Use when you know |
|---|---|
| v = u + at | u, a, t (find v) |
| s = ut + ½at² | u, a, t (find s) |
| v² = u² + 2as | u, v, a (find s) without t |
A worked example
A car starts from rest (u = 0) and accelerates at 2 m/s² for 5 s. Then v = 0 + 2 × 5 = 10 m/s, and s = 0 + ½ × 2 × 5² = 25 m. A car at 72 km/h is moving at 72 × 5/18 = 20 m/s.
u, v, a, t, s.
That has the unknown.
SI units.
Sensible size and unit?
Graphs of motion
On a distance–time graph, the slope is the speed. A straight sloping line means uniform speed, and a horizontal line means the object is at rest. On a velocity–time graph, the slope is the acceleration and the area under the graph is the displacement. In uniform circular motion, the speed is constant but the velocity changes because the direction changes, so there is acceleration.
Worked examples and common mistakes
Example: A runner goes round a 400 m track once. Distance = 400 m and displacement = 0. Example: A ball thrown upwards at 20 m/s with a = −10 m/s² stops rising when v = 0: t = 2 s. Common mistakes: mixing up speed and velocity, forgetting to convert km/h to m/s, and using negative acceleration without a sign convention.
Check your understanding: model answers
1. 36 × 5/18 = 10 m/s. 2. v = 4 + 3 × 2 = 10 m/s. 3. The displacement.
✨ Key Takeaways
- Displacement has a direction, but distance does not.
- Speed = distance ÷ time; velocity uses displacement.
- a = (v − u) ÷ t.
- The slope of a velocity–time graph is acceleration.
💬 Questions for Discussion & Reflection
- Convert 36 km/h to m/s.
- A body at 4 m/s accelerates at 3 m/s² for 2 s. Find v.
- What does the area under a velocity–time graph give?