On a distance-time graph the slope is speed. On a velocity-time graph the slope is acceleration and the area under the line is distance.
This lesson follows calculating speed, velocity and acceleration. It sits in the force and motion topic.
What do slope, flat lines and area mean?
| Feature | Distance-time graph | Velocity-time graph |
|---|---|---|
| Sloping line | Constant speed | Constant acceleration |
| Flat line | Not moving | Constant velocity, no acceleration |
| Steeper line | Faster | Greater acceleration |
| Area under line | Not used | Distance travelled |
The same shape means different things on the two graphs. Check the axis labels before you read anything.
Worked example: an invented toy car
A toy car’s velocity-time graph has three stages. From 0 to 4 s the velocity rises steadily from 0 to 6 m/s. From 4 to 10 s it stays at 6 m/s. From 10 to 12 s it falls steadily to 0.
Acceleration in stage 1. Slope = change in velocity ÷ time = 6 ÷ 4 = 1.5 m/s².
Stage 2. The line is flat, so the acceleration is zero and the car moves at a constant 6 m/s.
Distance in stage 2. Area of the rectangle = 6 × 6 = 36 m.
Total distance. Stage 1 is a triangle: ½ × 4 × 6 = 12 m. Stage 3 is a triangle: ½ × 2 × 6 = 6 m. Total = 12 + 36 + 6 = 54 m.
Check: the whole shape is a trapezium with parallel sides 12 s and 6 s and height 6. The area is ½ × (12 + 6) × 6 = 54 m. The two methods agree.
The mistake that costs marks
The usual slip is to read the height of the line. A student asked for the acceleration in stage 1 writes “6 m/s²” because the line reaches 6.
Height gives the velocity at that moment, in m/s. The acceleration needs the slope, 6 ÷ 4, because it asks how quickly the velocity changed. The unit m/s² is a clue: it means dividing by time.
Check yourself
An invented scooter has a velocity-time graph that rises from 0 to 10 m/s in 5 s, then stays at 10 m/s for 3 s. Find the acceleration in the first stage and the total distance.
Answer
Acceleration = 10 ÷ 5 = 2 m/s².
Distance in stage 1 = ½ × 5 × 10 = 25 m. Distance in stage 2 = 10 × 3 = 30 m.
Total distance = 25 + 30 = 55 m.
What to study next
Go on to applying force and momentum relationships, which explains why a velocity changes at all. Practise drawing your own graphs with the motion-graph explorer.
The graph evidence and fair-comparison lab gives more graph reading tasks. If you want a teacher to read your graph answers with you, see online one-to-one Science tuition.