Two speed–time graphs can show the same distance even if one reaches a much higher speed. Find the area under each graph over the stated time interval. For average speed, divide the distance by the total time for that trip.
The 2027 SEC G3 Mathematics syllabus (K310) includes interpreting speed–time graphs. The original example below compares a triangle with a rectangle and then adds a stationary interval.
- Read speed and time units first.
- Compare areas before comparing peak speeds.
- Use the time interval specified by the question.
Worked example | A triangle and a rectangle
Trip A lasts 12 seconds. Its speed rises steadily from 0 to 8 m/s in the first six seconds and falls steadily to 0 over the next six seconds. Its graph is a triangle with base 12 s and height 8 m/s, so its area represents ½ × 12 × 8 = 48 m.
Trip B moves at 3 m/s for 16 seconds. Its graph is a rectangle with area 16 × 3 = 48 m. The trips cover the same distance. Trip A reaches a higher speed and finishes sooner.
| Trip | Area shape | Elapsed time | Distance |
|---|---|---|---|
| A | Triangle | 12 s | 48 m |
| B | Rectangle | 16 s | 48 m |
Average speed is 48 ÷ 12 = 4 m/s for A and 48 ÷ 16 = 3 m/s for B. The two calculations use the same numerator and different denominators.
Include a stop when the question asks for elapsed time
Now add a four-second stop after Trip A comes to rest and ask for the average speed over all 16 seconds. During the stop, the speed is zero, so the extra section adds no area. The distance remains 48 m. The average over the full interval is 48 ÷ 16 = 3 m/s.
If asked for the average over only the first 12 seconds, keep 12 in the denominator. Mark the start and end of the requested interval before calculating.
Practise splitting a trapezium
A scooter travels at 2 m/s initially and increases its speed steadily to 6 m/s over 10 seconds. A rectangle of height 2 m/s gives 20 m. A triangle of height 4 m/s gives another 20 m. The total is 40 m.
A steady speed of 5 m/s covers the same 40 m in eight seconds. Ask a study partner to explain why a comparison of just 6 m/s and 5 m/s would miss the difference in time and graph shape.
Frequently asked questions
Does gradient give distance?
On a speed–time graph, area gives distance. The gradient describes how speed changes with time.
What if the time is in minutes and speed in metres per second?
Convert minutes to seconds before using the area to obtain metres.
Official information
SEAB’s 2027 SEC G3 Mathematics syllabus (K310), Problems in Real World Contexts and Rate and Speed. Checked 9 November 2026.