Equations of motion

For constant acceleration, the equations of motion link displacement, initial and final velocity, acceleration and time. They work for cars, falling objects and anything with steady acceleration.

Key facts

  • v = u + at
  • s = ut + ½at²
  • v² = u² + 2as
  • Free fall near Earth: a = g ≈ 9.8 m/s².
  • Pick the equation that has the three things you know and the one you want.

Worked examples

Example 1

A ball is dropped from 20 m. How fast is it going when it hits the ground?

  1. u = 0, a = 9.8, s = 20.
  2. v² = 0 + 2 × 9.8 × 20 = 392 v ≈ 19.8 m/s

Answer: 19.8 m/s