On a distance-time graph, the gradient is the speed. A flat line means the object is stopped, and a line sloping back down means it is returning.
This lesson opens the SPM Mathematics motion graphs chapter. The speed-time graphs lesson follows it.
How do you read speed from the line?
Pick two points on a straight section. Divide the change in distance by the change in time.
Speed = (distance₂ − distance₁) ÷ (time₂ − time₁). A steeper section means a faster speed.
Worked example: a cycle to the park
Aina cycles from home to a park and back. The graph shows distance from home in km against time in minutes:
| Stage | Points | What happens |
|---|---|---|
| A | (0, 0) to (20, 5) | Cycles away from home |
| B | (20, 5) to (30, 5) | Distance stays at 5 km |
| C | (30, 5) to (60, 0) | Returns home |
Stage A. Speed = 5 ÷ 20 = 0.25 km per minute. Multiply by 60 to get 15 km/h.
Stage B. The line is flat, so the distance from home does not change. Aina is resting, and the speed is 0.
Stage C. The distance falls by 5 km in 30 minutes, so the speed is 5 ÷ 30 = 1/6 km per minute, which is 10 km/h. The line slopes downward because she is coming back, but speed itself is positive.
The total distance travelled is 5 + 5 = 10 km, although she ends at distance 0 from home.
The mistake that costs marks
The common slip is to read the flat line as “moving at a steady speed”. On a distance-time graph, a steady speed is a straight sloping line, and a flat line is a stop.
| Wrong | Right | |
|---|---|---|
| Stage B | Steady movement | Stopped, speed 0 |
| Stage C speed | −10 km/h | 10 km/h heading home |
| Total distance | 0 km | 10 km |
Ask yourself two questions for every section: is the distance changing, and in which direction?
Check yourself
A van travels from a depot. The graph has points (0, 0), (2, 80), (2.5, 80) and (4, 155), with time in hours and distance in km. Find the speed in each stage and the average speed for the whole journey.
Answer
Stage 1, from (0, 0) to (2, 80): 80 ÷ 2 = 40 km/h.
Stage 2, from (2, 80) to (2.5, 80): the distance is unchanged, so the van is stopped.
Stage 3, from (2.5, 80) to (4, 155): 75 ÷ 1.5 = 50 km/h.
Average speed = 155 ÷ 4 = 38.75 km/h. The stop time is included in the 4 hours.
What to study next
Move to reading speed-time graphs, where the slope means something different. You can compare line shapes in the graph evidence and fair-comparison lab. Log slips in the mistake log and paper-error review.
If you want a teacher to go through your graph readings, see online one-to-one Mathematics tuition.