Motion graphs look similar, but distance–time and velocity–time graphs tell you very different things. Mixing them up is one of the most common mistakes in the forces topic.
Distance–time graphs
- The gradient (steepness) = speed.
- A flat line means the object is stationary.
- A straight sloping line means constant speed.
- A curve means the speed is changing. To find the speed at one moment, draw a tangent and find its gradient.
Velocity–time graphs
- The gradient = acceleration.
- A flat line means constant velocity (not stationary!).
- A line sloping down means the object is decelerating.
- The area under the graph = distance travelled.
Worked example
A cyclist speeds up steadily from rest to 12 m/s in 4 s. Find the acceleration and the distance travelled.
- Acceleration = gradient = change in velocity ÷ time = 12 ÷ 4 = 3 m/s²
- The graph makes a triangle, so distance = area = ½ × base × height
- Distance = ½ × 4 × 12 = 24 m
Top tips
- Always check the y-axis label before you answer anything.
- When finding a gradient, use a big triangle to reduce reading errors.
- For areas, split complicated shapes into rectangles and triangles.
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