A speed-time graph shows how the speed of an object changes with time. This subtopic covers acceleration as the gradient and distance as the area under the graph.
Reading the graph
Time is on the horizontal axis and speed on the vertical axis. The gradient gives the acceleration.
Key formula
$\text{acceleration} = \text{gradient} = \frac{\text{change in speed}}{\text{time}}$
- An upward slope means acceleration (speeding up).
- A downward slope means deceleration (slowing down); its gradient is negative.
- A horizontal line means constant speed (zero acceleration).
Distance = area under the graph
The distance travelled equals the area between the graph and the time axis. Split the area into rectangles and triangles.
Key formula
$\text{distance} = \text{area under the speed-time graph}$
Example
A car accelerates uniformly from $0$ to $30$ m/s in $10$ s. Acceleration $=\dfrac{30}{10}=3$ m/s$^2$; distance $=\tfrac12\times10\times30=150$ m (area of a triangle).
Remember
Gradient = acceleration; area under the line = distance. A flat line means constant speed.