Velocity and acceleration

Velocity is speed in a given direction. Acceleration is how quickly velocity changes. Velocity–time graphs show both: the gradient is acceleration and the area is distance travelled.

Key facts

  • Acceleration = change in velocity ÷ time (m/s²).
  • Velocity–time graph: gradient = acceleration; area under = distance.
  • A horizontal line means constant velocity; a sloping line means accelerating.
  • Negative acceleration means slowing down (deceleration).

Worked examples

Example 1

A car speeds up steadily from 0 to 20 m/s in 8 s, then stays at 20 m/s for 10 s. How far does it go?

  1. Triangle: ½ × 8 × 20 = 80 m.
  2. Rectangle: 10 × 20 = 200 m.
  3. Total: 280 m.

Answer: 280 m