Distance–Time Graphs

A distance–time graph shows how far an object is from a starting point as time passes. It helps you describe motion without seeing the journey.

Axes and what the graph means

• Horizontal axis (x‑axis): time (s, min, h)
• Vertical axis (y‑axis): distance from the start (m, km)
• Each point tells you the distance at a particular time.

Speed from the slope (gradient)

Speed is how fast distance changes. On a distance–time graph, speed equals the slope of the line.

Use:

$$\text{speed} = \text{slope} = \frac{\Delta s}{\Delta t} \quad (\text{units, e.g. m/s or km/h})$$

Average speed over a whole trip:

$\text{average speed} = \dfrac{\text{total distance}}{\text{total time}}$

What different lines tell you

• Horizontal line: slope = 0 → at rest (distance not changing).
• Straight sloping line: constant speed (same slope everywhere on that line).
• Steeper line: faster speed.
• Curve getting steeper: speeding up (accelerating).
• Curve getting less steep: slowing down (decelerating).
• Line sloping downwards: distance from the start is decreasing (moving back towards the start). Speed is the size of the slope.

Common misconceptions

• The area under a distance–time graph does not give a useful quantity (area is only used with speed–time graphs to find distance).
• A vertical line would mean an instant jump in distance (infinite speed). This is not physically possible.
• Negative slope does not mean negative speed; it means moving back towards the start.
• Keep units consistent. If distance is in km and time in h, the speed is in km/h.