A distance-time graph shows how far an object is from a starting point at each moment. This subtopic covers reading such graphs, speed as gradient, and stationary/return motion.
Reading the graph
Time is on the horizontal axis and distance on the vertical axis. The gradient (slope) of the line gives the speed.
Key formula
$\text{speed} = \text{gradient} = \frac{\text{distance}}{\text{time}}$
Shapes of the line
- A steeper line means a greater speed.
- A horizontal line means the object is stationary (at rest) — distance is not changing.
- A line sloping down towards the time axis means the object is returning to the start.
Example
An object travels $150$ m in $30$ s at constant speed. Speed $= \dfrac{150}{30} = 5$ m/s, so the graph is a straight line with gradient $5$.
Finding distance and time
Rearrange the formula: $\text{distance} = \text{speed} \times \text{time}$ and $\text{time} = \dfrac{\text{distance}}{\text{speed}}$.
Remember
On a distance-time graph, gradient = speed. Flat line = at rest; downward line = coming back.