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
The next step is that the area under the same graph gives distance, which is covered in 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, online one-to-one Physics tuition gives a teacher the chance to check your working step by step.