Constant acceleration (SUVAT)

When acceleration is constant, five quantities describe the motion: displacement s, initial velocity u, final velocity v, acceleration a and time t. Five equations link them, each missing one quantity.

Key facts

  • v = u + at (no s)
  • s = ut + ½at² (no v)
  • s = vt − ½at² (no u)
  • v² = u² + 2as (no t)
  • s = ½(u + v)t (no a)
  • Choose a positive direction; for free fall a = 9.8 m/s² downwards.

Worked examples

Example 1

A car accelerates from 5 m/s to 25 m/s over 100 m. Find its acceleration.

  1. u = 5, v = 25, s = 100. Use v² = u² + 2as.
  2. 625 = 25 + 200a a = 3 m/s²

Answer: 3 m/s²

Example 2

A stone is dropped from 45 m. How long does it take to land? (g = 9.8)

  1. u = 0, a = 9.8, s = 45.
  2. 45 = 4.9t² t = 3.03 s

Answer: 3.03 s