Acceleration = change in speed ÷ time taken. On a speed-time graph, this is the gradient of the line, found by “rise over run”.
This lesson follows comparing distance-time and speed-time graphs, and it is a central skill in motion and graphs.
What does acceleration measure?
Acceleration measures how quickly speed changes. A car that goes from 0 to 20 m/s in 10 s has a steady rate of change of 2 m/s every second. That is an acceleration of 2 m/s².
If speed decreases, the change is negative. The object is slowing down, and the gradient of the graph slopes downward.
How do I find it step by step?
- Choose two points on a straight part of the line, far apart so reading errors matter less.
- Read the speed and time at each point.
- Find the change in speed (later speed minus earlier speed).
- Find the change in time (later time minus earlier time).
- Divide change in speed by change in time, and give the unit m/s².
Worked example
Here is an invented speed-time graph for a scooter. Speed goes from 0 to 12 m/s between 0 s and 6 s, stays at 12 m/s until 14 s, then falls to 0 m/s at 18 s.
0 to 6 s: change in speed = 12 − 0 = 12 m/s. Time = 6 s. Acceleration = 12 ÷ 6 = 2 m/s².
6 to 14 s: speed does not change, so the gradient is 0. Acceleration = 0 m/s². The scooter moves at constant speed.
14 to 18 s: change in speed = 0 − 12 = −12 m/s. Time = 18 − 14 = 4 s. Acceleration = −12 ÷ 4 = −3 m/s². The scooter decelerates at 3 m/s².
Check for sense: the stopping phase is shorter than the speeding-up phase but covers the same change in speed, so its rate must be larger in size. It is (3 against 2).
The mistake to watch for
A student is asked for the acceleration when speed goes from 4 m/s to 16 m/s over 6 s.
Mistaken answer: 16 ÷ 6 = 2.67 m/s.
This divides the final speed by the time, which ignores that the object was already moving at 4 m/s. The unit is also wrong.
Correction: the change in speed is 16 − 4 = 12 m/s. Acceleration = 12 ÷ 6 = 2 m/s². Using only the final speed is correct only when the object starts from rest.
Check yourself
Try these, then open each answer.
1. A cyclist’s speed rises from 10 m/s to 30 m/s in 5 s. Find the acceleration.
Show answer
Change in speed = 30 − 10 = 20 m/s. Acceleration = 20 ÷ 5 = 4 m/s².
2. A car slows from 25 m/s to 5 m/s in 10 s. Find the acceleration and describe it in words.
Show answer
Change in speed = 5 − 25 = −20 m/s. Acceleration = −20 ÷ 10 = −2 m/s². The car decelerates at 2 m/s².
3. Two points on a straight line of a speed-time graph are (2 s, 6 m/s) and (8 s, 18 m/s). Find the gradient and say what it represents.
Show answer
Gradient = (18 − 6) ÷ (8 − 2) = 12 ÷ 6 = 2 m/s². It represents the acceleration, which is constant because the line is straight.
Where this leads next
Next, the area under the same graph gives distance. See interpreting area under a speed-time graph. The bounds and rounding explainer is helpful when your graph readings are only accurate to a stated precision.
If you can calculate acceleration but still hesitate over signs and units, a teacher in online one-to-one Physics tuition can check your working step by step.