Motion is the change in position of an object with time. To describe motion, we use three key quantities: speed, velocity and acceleration.
Speed and Velocity
- Speed = distance ÷ time. It is a scalar quantity (has magnitude only).
- Velocity = displacement ÷ time. It is a vector quantity (has magnitude and direction).
Average speed = total distance travelled ÷ total time taken.
Key difference: Speed has no direction; velocity has direction. If an object changes direction, its velocity changes even if its speed stays the same.
Acceleration
Acceleration is the rate of change of velocity.
Acceleration (a) = change in velocity ÷ time taken = (v − u) ÷ t
- u = initial velocity, v = final velocity, t = time.
- Unit: metre per second squared (m/s²).
- Negative acceleration is called deceleration or retardation.
Equations of Uniformly Accelerated Motion
| Equation | Used to find |
|---|---|
| v = u + at | final velocity |
| s = ut + ½at² | distance (when u, a, t known) |
| v² = u² + 2as | final velocity (without time) |
| s = (u + v)/2 × t | distance (average velocity × time) |
Worked Example
A car accelerates from rest to 20 m/s in 5 s. Find its acceleration and the distance covered.
- Acceleration: a = (v − u)/t = (20 − 0)/5 = 4 m/s²
- Distance: s = ut + ½at² = 0 + ½ × 4 × 25 = 50 m
Summary
Speed is scalar, velocity is a vector. Acceleration is the rate of change of velocity. Use the four equations of uniformly accelerated motion to solve problems — memorise them and practise the worked example above.
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