The idea
The symbols are displacement s, initial velocity u, final velocity v, acceleration a and time t. Useful equations include v = u + at, s = ut + ½at² and v² = u² + 2as. Choose the equation that uses the quantities you know and avoids the unknown you do not need. For vertical motion near Earth, free-fall acceleration is approximately 9.81 m/s² downward when air resistance is negligible.
Worked example
A car starts from rest and accelerates uniformly at 2 m/s² for 5 s. Find its final speed and displacement.
- u = 0, a = 2 m/s² and t = 5 s.
- v = 0 + 2 × 5 = 10 m/s.
- s = 0 × 5 + ½ × 2 × 5² = 25 m.
A mistake to avoid
A negative acceleration does not always mean slowing down. An object speeds up when velocity and acceleration have the same sign.
Check your understanding
A bike slows from 12 m/s to 4 m/s in 4 s. Find its acceleration.
Show the explanation
a = (4 − 12) ÷ 4 = −2 m/s², taking the original direction of travel as positive.
Explore the lesson
This guide connects to Speeding Up, Slowing Down, and Falling in the IB Physics course. The first two published lessons per subject are free previews; further interactive lessons require an account.