A distance-time graph and a speed-time graph look almost the same on the page, and that is exactly why so many IGCSE Physics students mix them up. A flat line means something completely different on each one. This guide explains both types of graph for Cambridge IGCSE Physics (0625) with one worked example you can follow from start to finish, plus the mistakes that quietly cost marks.
The one rule that stops most mistakes
Before you read anything off a graph, look at the y-axis label. Is it distance or speed?
- On a distance-time graph, the gradient (steepness) gives the speed.
- On a speed-time graph, the gradient gives the acceleration, and the area under the graph gives the distance travelled.
Everything else follows from those three facts.
Distance-time graphs
On a distance-time graph, time is on the x-axis and distance from the start is on the y-axis.
| What you see | What it means |
|---|---|
| Straight sloping line | Constant speed |
| Steeper line | Faster speed |
| Horizontal line | Stationary (not moving) |
| Curve getting steeper | Accelerating |
| Curve getting flatter | Decelerating |
| Line sloping downwards | Moving back towards the start |
To find the speed, calculate the gradient:
speed = distance ÷ time
If a cyclist's line goes from 0 m at 0 s to 60 m at 10 s, the speed is 60 ÷ 10 = 6 m/s.
Tip: A horizontal line on a distance-time graph does not mean the object is moving steadily. It means the object has stopped, because its distance is not changing.
For a curved line, Extended candidates may be asked to find the speed at one instant. Draw a tangent to the curve at that point, then find the gradient of the tangent. Draw it as long as you can, and use a ruler, because a short, wobbly tangent gives an inaccurate answer.
Speed-time graphs
On a speed-time graph, the y-axis shows how fast the object is moving at each moment.
| What you see | What it means |
|---|---|
| Straight sloping line upwards | Constant acceleration |
| Horizontal line (above zero) | Constant speed, zero acceleration |
| Straight sloping line downwards | Constant deceleration |
| Horizontal line on the x-axis | Stationary |
| Curve getting steeper | Increasing acceleration |
Two calculations matter:
- 1Acceleration = change in speed ÷ time taken. This is the gradient.
- 2Distance = area under the graph. For shapes made of rectangles and triangles, work out each area and add them.
Worked example: a car's journey
Question (written by us, in the style of IGCSE): A car starts from rest. Its speed increases steadily to 12 m/s in 6 s. It then travels at 12 m/s for 10 s. It then slows steadily to a stop in 4 s. (a) Calculate the acceleration in the first 6 s. (b) Calculate the total distance travelled. (c) Calculate the average speed for the whole journey.
Sketch the graph first. It has three sections: a sloping line up, a flat line, then a sloping line down to zero.
Part (a): acceleration in the first section
acceleration = change in speed ÷ time = (12 − 0) ÷ 6 = 2 m/s²
Part (b): total distance
Split the area into a triangle, a rectangle and another triangle.
- Section 1 (triangle): ½ × 6 × 12 = 36 m
- Section 2 (rectangle): 12 × 10 = 120 m
- Section 3 (triangle): ½ × 4 × 12 = 24 m
Total distance = 36 + 120 + 24 = 180 m
Part (c): average speed
Total time = 6 + 10 + 4 = 20 s
average speed = total distance ÷ total time = 180 ÷ 20 = 9 m/s
Notice that the average speed (9 m/s) is lower than the top speed (12 m/s). That makes sense, because the car spent some of the journey speeding up and slowing down. If your average speed came out higher than the maximum speed on the graph, you know there is a mistake.
Tip: Always write the formula, the substitution and the answer with its unit. Even if your arithmetic slips, the method marks can still be earned.
Deceleration and negative acceleration
For the final section of the car's journey, the acceleration is (0 − 12) ÷ 4 = −3 m/s². The negative sign shows the car is slowing down. In an exam, you can say either "acceleration of −3 m/s²" or "deceleration of 3 m/s²". Both are accepted if you are clear about which you mean.
Six common mistakes to avoid
- 1Reading the wrong graph. Always check the y-axis label before you start.
- 2Using the height of the graph as the distance. On a speed-time graph, distance is the area, not the height.
- 3Forgetting units. Speed is m/s, acceleration is m/s², distance is m.
- 4Mixing minutes and seconds. Convert to seconds before you calculate.
- 5Calling a flat speed-time line "stopped". It means constant speed unless it sits on the x-axis.
- 6Giving a tiny tangent. For curves, a short tangent makes the gradient unreliable.
Free fall and the number 10
In IGCSE Physics, the acceleration of free fall near the Earth's surface is taken as about 10 m/s² (equivalent to a gravitational field strength of 10 N/kg). On a speed-time graph, an object falling freely with negligible air resistance gives a straight line with a gradient of about 10. With air resistance, the line curves and flattens as the object approaches terminal velocity. Check the motion section of the Cambridge IGCSE Physics 0625 syllabus for exactly what you are expected to know at Core and Extended level.
How to practise this topic
Graphs are a skill, and skills need practice rather than reading. A good routine is:
- 1Draw a simple journey in words, such as "accelerates for 5 s, steady for 8 s, brakes for 3 s".
- 2Sketch both the distance-time and speed-time graph for it.
- 3Calculate the acceleration and distance for each section.
- 4Swap your journey with a friend and mark each other's work.
Recalling and applying the method from memory, rather than re-reading it, is far more effective for long-term learning (Roediger & Karpicke, 2006). Spreading these sessions across several days helps even more (Cepeda et al., 2006). If you are planning that spread, our guide on building an IGCSE study plan shows how to work backwards from your exam dates.
A good test of whether you really understand this topic is whether you can explain it. Try teaching a friend why the area under a speed-time graph gives distance. If you get stuck, you have found your gap. We cover why this works in why teaching a topic is the fastest way to learn it.
Where TeachVerse fits
TeachVerse is a study app for Cambridge IGCSE where you learn by teaching: you explain a topic, such as motion graphs, to your own AI pupil, which only knows what you taught it and then answers exam-style questions. If your explanation of gradient and area is muddled, the pupil's answers show it. You can then follow up with topical papers and mark schemes, flashcards and quizzes. The questions are original and written in the style of Cambridge IGCSE papers, and TeachVerse is not affiliated with or endorsed by Cambridge. Try it free or compare plans.
Sources: Cambridge International, IGCSE Physics 0625 syllabus; Roediger, H. L. & Karpicke, J. D. (2006), Psychological Science; Cepeda, N. J., Pashler, H., Vul, E., Wixted, J. T. & Rohrer, D. (2006), Psychological Bulletin.