A distance-time graph shows how far an object has gone. A speed-time graph shows how fast it is going. The same journey gives two different-looking graphs, and you must read the axis labels before choosing a rule.
This lesson builds on calculating speed over a segment and prepares for finding acceleration from a gradient in motion and graphs.
What does each graph show?
| Feature | Distance-time graph | Speed-time graph |
|---|---|---|
| Vertical axis | Distance travelled | Speed |
| Gradient | Speed | Acceleration |
| Horizontal line | At rest | Constant speed |
| Straight sloping line | Constant speed | Constant acceleration |
| Area under the line | No useful meaning | Distance travelled |
The same shape means different things on the two graphs, which is why students mix them up.
How do I compare them step by step?
- Read both axis labels and their units.
- Split the graph into segments where the line changes direction or steepness.
- Describe each segment in words using the table above.
- Match the descriptions: a segment described as “constant speed” gives a straight slope on the first graph and a flat line on the second.
Worked example
Invented motion for a trolley on a track. From 0 to 4 s it moves at 3 m/s. From 4 to 8 s it is stationary.
From 8 to 12 s it moves again at 3 m/s, in the same direction as at first.
Distance-time graph:
- 0 to 4 s: distance rises from 0 m to 12 m (3 × 4 = 12). Straight line, gradient 12 ÷ 4 = 3 m/s.
- 4 to 8 s: distance stays at 12 m. Horizontal line, gradient 0.
- 8 to 12 s: distance rises from 12 m to 24 m (3 × 4 = 12). Gradient 12 ÷ 4 = 3 m/s.
Speed-time graph:
- 0 to 4 s: horizontal line at 3 m/s.
- 4 to 8 s: line along the time axis at 0 m/s.
- 8 to 12 s: horizontal line at 3 m/s.
Both graphs tell the same story. On the first, the stop is a flat line; on the second, the stop is a line sitting at zero. The moving parts are sloped on the first and flat on the second.
The mistake to watch for
A student sees a graph with a long horizontal section and answers “the object is stationary”.
Mistaken answer: “The horizontal line from 10 s to 30 s shows the object is at rest.”
The student forgot to check the vertical axis. It was labelled “speed (m/s)”, and the line was at 6 m/s.
Correction: on a speed-time graph, a horizontal line at 6 m/s means constant speed of 6 m/s. Rest would be a line at 0 m/s. A quick habit helps: before answering, say aloud “this graph’s vertical axis is…” and complete the sentence.
Check yourself
Try these, then open each answer.
1. A distance-time graph goes in a straight line from (0 s, 0 m) to (10 s, 50 m), then stays flat until 20 s. Describe the motion and give the speed in the first 10 s.
Show answer
For the first 10 s the object moves at constant speed: 50 ÷ 10 = 5 m/s. From 10 s to 20 s the distance does not change, so the object is at rest.
2. On a speed-time graph, a horizontal line is drawn at 5 m/s from 0 s to 8 s. How far does the object travel, and what would its distance-time graph look like for this time?
Show answer
Distance = 5 × 8 = 40 m. The distance-time graph is a straight sloping line from (0, 0) to (8, 40), with gradient 5 m/s.
3. A straight sloping line on a speed-time graph rises from 0 to 12 m/s over 6 s. What shape is its distance-time graph?
Show answer
Speed is increasing steadily, so the distance covered each second grows. The distance-time graph is a curve that gets steeper.
Where this leads next
Next, see how the gradient of a speed-time graph gives acceleration in finding acceleration from a gradient. The graph-model and residual explorer and the rate and energy graph interpreter are useful for practising what a gradient means on a labelled graph.
If you keep choosing the right rule for the wrong graph, online one-to-one Physics tuition lets a teacher hear your reasoning and fix it at the point it slips.