What is acceleration?
Acceleration measures how quickly the velocity of an object changes. When an object speeds up, it has positive acceleration; when it slows down, the acceleration is negative (also called deceleration). The unit is metres per second per second, written m/s².
Key idea
Acceleration = (final velocity − initial velocity) ÷ time taken. A result of 5 m/s² means the velocity rises by 5 m/s every second.
Working it out
Worked example
A car speeds up from 0 to 20 m/s in 4 seconds. Find its acceleration.
a = (20 − 0) ÷ 4 = 20 ÷ 4 = 5 m/s².
A second car slows from 25 m/s to 5 m/s in 4 s: a = (5 − 25) ÷ 4 = −20 ÷ 4 = −5 m/s² (deceleration).
The speed-time graph
On a speed-time graph, time is along the bottom and speed goes up the side. The gradient (steepness) of the line gives the acceleration. A horizontal line means constant speed, so the acceleration is zero. A line sloping up shows acceleration; a line sloping down shows deceleration.
The area under a speed-time graph gives the distance travelled. For a rectangle of height 10 m/s and width 6 s, the distance is 10 × 6 = 60 m. The steeper the line, the greater the acceleration.
When you work out an acceleration, always subtract the initial velocity from the final velocity first, then divide by the time. If the answer comes out negative, the object is slowing down.
Remember
- Acceleration = change in velocity ÷ time.
- Slowing down gives a negative value.
- Flat speed-time line → zero acceleration; area under it → distance.