A speed-time graph puts time along the bottom and speed up the side. It looks like a distance-time graph, but it tells a different story. Here the slope is the change in speed per second: the acceleration.
Key idea
On a speed-time graph: a rising line means speeding up, a flat line means a steady speed, a falling line means slowing down, and a line along the time axis means stopped. Slope = acceleration.
Why it works
Over any piece of the graph, the rise is a change in speed and the run is a time, so rise ÷ run is $\dfrac{\Delta v}{\Delta t}$, the acceleration. A flat line has zero rise: the speed is not changing, but it is not zero either, so the object keeps moving.
Worked example: Acceleration from the slope
A speed-time graph rises in a straight line from 2 m/s at 0 s to 14 m/s at 4 s. Find the acceleration.
- Rise: $14 - 2 = 12$ m/s.
- Run: $4 - 0 = 4$ s.
- Slope: $a = \dfrac{12\,\mathrm{m/s}}{4\,\mathrm{s}} = 3\,\mathrm{m/s^2}$.
Answer: $3\,\mathrm{m/s^2}$
Worked example: A flat stretch
A speed-time graph is flat at 8 m/s from 4 s to 10 s. What is happening, and how far does the object go?
- Flat line: the speed stays 8 m/s, so the acceleration is 0.
- The object is still moving: distance $= s\,t = 8\,\mathrm{m/s} \times 6\,\mathrm{s} = 48\,\mathrm{m}$.
- That is the area of the rectangle under the line, 8 tall and 6 wide.
Answer: Steady speed; 48 m
Common mistake
Mixing up the two graphs. A flat line on a distance-time graph means stopped. A flat line on a speed-time graph means moving at a steady speed. Check the label on the side axis before you read the shape.
| Shape of the line | Distance-time graph | Speed-time graph |
|---|---|---|
| Flat | Stopped | Steady speed |
| Straight, rising | Steady speed | Speeding up steadily |
| Falling | (not possible: distance never shrinks) | Slowing down |