Distance-Time Graphs

Interpreting Distance-Time Graphs

A distance-time graph shows how the distance travelled by an object changes over time. The horizontal axis (x-axis) represents time, usually in seconds (s), and the vertical axis (y-axis) represents distance from the starting point, usually in metres (m).

The shape of the graph tells you about the motion of the object:

• A flat (horizontal) line means the object is stationary — it is not moving, so the distance does not change over time.
• A straight sloping line means the object is moving at a constant speed.
• A curved line means the speed is changing — the object is accelerating or decelerating.
• The steepness (gradient) of the line shows how fast the object is moving. A steeper line means a higher speed.

For example, if a graph shows a line rising steadily from 0 m at 0 s to 100 m at 20 s, the object is moving away from the start at a steady speed.

Types of Motion on Graphs

Different types of motion produce different shapes on a distance-time graph:

• Straight line (diagonal): The object moves at a constant speed. The distance increases evenly over time.
• Curved line: The speed is changing. If the curve gets steeper, the object is speeding up. If it gets less steep, the object is slowing down.
• Horizontal line: The object is stationary. Distance does not change with time.

For example, a cyclist pedalling at a steady speed will produce a straight diagonal line. If they stop to rest, the graph will flatten out. When they start pedalling again, the graph will slope upwards again.

Calculating Speed from Graphs

Speed is how fast something moves and is calculated by dividing the distance travelled by the time taken:

Speed = $\frac{\text{distance}}{\text{time}}$

On a distance-time graph, speed is found by calculating the gradient (steepness) of the line:

Gradient = $\frac{\text{rise}}{\text{run}} = \frac{\text{change in distance}}{\text{change in time}}$

A steeper gradient means a higher speed.

For instance, if the distance increases by 60 metres over 20 seconds, the speed is:

$$\text{Speed} = \frac{60 \text{ m}}{20 \text{ s}} = 3 \text{ m/s}$$