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A cyclist has travelled 20 metres. Ten seconds later, the distance–time graph still shows 20 metres. What happened during those ten seconds?
The cyclist stopped. Time kept passing, but the total distance travelled stayed the same. That’s why the line went flat.
If you’re preparing for Cambridge IGCSE Physics (0625), start by asking two questions when you see a distance–time graph. How much did the distance change? How long did that change take? Those two readings let you calculate speed on any straight section of the graph. Cambridge IGCSE Physics syllabus
What does the shape of a distance–time graph tell you?
Time goes on the horizontal axis. Total distance travelled goes on the vertical axis. Check the units on both axes before you read the graph.
| Shape of the line | What it tells you |
|---|---|
| Horizontal | The object is stopped. Time passes while distance stays the same. |
| Straight and rising | The object moves at a constant speed. It covers equal distances in equal times. |
| Steeper straight section | The object moves faster on this section of the same graph. |
| Curve that gets steeper | The object’s speed is increasing. |
Worked example — a cyclist moves, stops and moves again
Imagine these four points are joined in order by straight lines on a distance–time graph.
| Time | Total distance travelled |
|---|---|
| 0 s | 0 m |
| 10 s | 20 m |
| 20 s | 20 m |
| 30 s | 60 m |
1. How fast was the cyclist moving in the first 10 seconds?
Use the gradient, or steepness, of that section.
Speed = change in distance ÷ change in time
From 0 to 10 seconds, the cyclist covers 20 metres. The speed is 20 ÷ 10 = 2 m/s.
2. What happened between 10 and 20 seconds?
The reading stays at 20 metres. The cyclist covers 0 additional metres during those 10 seconds, so their speed is 0 m/s. This section is horizontal.
3. How fast was the cyclist moving in the final 10 seconds?
Use the readings at the start and end of that section.
Distance covered = 60 − 20 = 40 m
Time taken = 30 − 20 = 10 s
Speed = 40 ÷ 10 = 4 m/s
The cyclist travels twice as fast in the final section as in the first. On the graph, the final section is twice as steep.
Why is the average speed only 2 m/s?
For the whole journey, divide the total distance travelled by the total elapsed time, including the stop.
Average speed = 60 m ÷ 30 s = 2 m/s
If the question asks for the average speed while the cyclist was moving, use only the 20 seconds spent moving. That gives 60 m ÷ 20 s = 3 m/s. Read the wording to see which time interval the question asks for.
Try it yourself
A second cyclist travels 15 metres in the first 5 seconds, stops for 5 seconds, then covers another 25 metres in the next 10 seconds.
What is the speed during the first 5 seconds?
Which time interval would be horizontal on a distance–time graph?
What is the average speed for the whole journey?
Answers — 1. 3 m/s. 2. 5 to 10 seconds. 3. 2 m/s, because the cyclist covers 40 metres in 20 seconds.
Parents can turn this into a short revision exercise by asking their child to sketch the second journey and point to the two coordinates they used for each calculation.
Frequently asked questions
Do I always start from zero when calculating the gradient?
Choose two points on the straight section the question asks about. Subtract the earlier distance reading from the later one, then do the same for the time readings.
What if the graph shows speed on the vertical axis?
Check the axis label before choosing a formula. A horizontal line on a speed–time graph shows constant speed. A horizontal line on a distance–time graph shows that the object is stopped.
For revision planning across subjects, read TheTuitionE’s IGCSE exam preparation guide for UAE parents.
If your child can recall the speed formula but gets stuck choosing which numbers to use, bring a recent graph question to a free TheTuitionE demo class.
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