On a speed-time graph, the gradient is the acceleration. A flat line at a height above zero means constant speed, and a line that falls means the object is slowing down.
This lesson follows reading distance-time graphs in the SPM Mathematics motion graphs chapter.
How do you read acceleration?
Choose two points on a straight section. Divide the change in speed by the change in time.
Acceleration = (speed₂ − speed₁) ÷ (time₂ − time₁). The unit is speed unit per time unit, so m/s divided by s gives m/s².
Worked example: a motorbike at a junction
The graph shows speed in m/s against time in seconds with points (0, 0), (8, 16), (20, 16) and (24, 4).
| Stage | Points | Reading |
|---|---|---|
| A | (0, 0) to (8, 16) | Speeding up |
| B | (8, 16) to (20, 16) | Constant speed |
| C | (20, 16) to (24, 4) | Slowing down |
Stage A. Acceleration = (16 − 0) ÷ (8 − 0) = 2 m/s².
Stage B. The speed does not change, so the acceleration is 0. The bike is moving at 16 m/s.
Stage C. Change in speed = 4 − 16 = −12 over 4 seconds, so the gradient is −3 m/s². The deceleration is 3 m/s².
The mistake that costs marks
The common slip is to carry over the distance-time rule and call the flat line in stage B “stopped”. On a speed-time graph, the height of the line is the speed. A line at height 16 means moving at 16 m/s.
| Distance-time graph | Speed-time graph | |
|---|---|---|
| Vertical axis | Distance | Speed |
| Flat line at height above 0 | Stopped | Constant speed |
| Gradient | Speed | Acceleration |
| Stopped | Flat line | Line on the time axis |
Before you read anything, say aloud what the vertical axis measures.
Check yourself
A speed-time graph has points (0, 5), (6, 35), (10, 35) and (14, 0), with speed in m/s and time in seconds. Find the acceleration in the first stage, the speed in the second stage, and the deceleration in the last stage.
Answer
First stage: (35 − 5) ÷ (6 − 0) = 30 ÷ 6 = 5 m/s².
Second stage: the line is flat at 35, so the speed is a constant 35 m/s.
Last stage: (0 − 35) ÷ (14 − 10) = −35 ÷ 4 = −8.75. The deceleration is 8.75 m/s².
What to study next
The area under this same graph gives distance. Continue with calculating distance from a speed-time graph. Change a journey in the motion-graph explorer and compare the graphs, then log slips in the mistake log and paper-error review.
If you want a teacher to check your readings, see online one-to-one Mathematics tuition.