Describing Motion Around Us
Acceleration
Measure how quickly velocity changes.
Start with what you feel. You are standing in a bus. When it starts suddenly, you jerk backwards. When it brakes hard, you lurch forwards. What you feel is the bus's velocity changing.
Acceleration: how quickly velocity changes. In words: acceleration = change in velocity ÷ time taken.
In symbols: a = (v – u) ÷ t, where
- u = the velocity at the start;
- v = the velocity at the end;
- t = the time between them.
'Change' always means end minus start: v – u.
The unit. Velocity is in m/s, and we divide by seconds again. So acceleration is in metres per second per second, written m s⁻².
Example: a cycle goes from 2 m/s to 6 m/s in 2 s. a = (6 – 2) ÷ 2 = 2 m s⁻²: it gains 2 m/s every second.
Speeding up or slowing down.
- Speeding up: v is bigger than u, so a is positive. The acceleration points the same way as the motion.
- Slowing down: v is smaller than u, so a is negative. The acceleration points against the motion.
Changing km/h into m/s. 1 km = 1000 m and 1 h = 3600 s. So 36 km h⁻¹ = 36 × 1000 ÷ 3600 = 10 m s⁻¹. In the same way, 54 km h⁻¹ = 15 m s⁻¹. Shortcut: multiply km/h by 5/18 (because 1000 ÷ 3600 = 5/18).
The bus, twice.
- It speeds up from 10 to 15 m s⁻¹ in 10 s: a = (15 – 10) ÷ 10 = 0.5 m s⁻².
- Later it brakes from 15 m s⁻¹ to a stop in 5 s: a = (0 – 15) ÷ 5 = –3 m s⁻². The minus sign means it is slowing down.
Fast is not the same as accelerating. Acceleration is about how quickly the velocity changes, not how fast you go. A bus going very fast at a steady velocity has zero acceleration: you feel no jerk at all.
Falling objects. Drop a stone. Every second it gains 9.8 m s⁻¹ of velocity. That is a constant acceleration of 9.8 m s⁻², called g. The Earth's pull causes it.
Practise this lesson
Questions that get harder as you improve, a Tutor that helps without giving the answer away, and progress you can see. Free for every learner.
No account, no email address. Opens the real product.