Reading Distance-Time Graphs

A distance-time graph shows how far an object has travelled over time. The gradient (slope) of the line gives the speed.

What do the features of the graph mean?

Feature	Meaning
Straight line with positive gradient	Constant speed
Horizontal line (zero gradient)	Stationary (not moving)
Steeper line	Higher speed
Curved line (getting steeper)	Accelerating
Curved line (getting flatter)	Decelerating

How do you calculate speed from the graph?

Speed equals the gradient of the distance-time graph:

$\text{speed} = \frac{\Delta s}{\Delta t} = \frac{\text{change in distance}}{\text{change in time}}$

Choose two points on the straight section of the line, read their coordinates, and divide the vertical change by the horizontal change.

Worked example

On a distance-time graph, an object moves from 20 m at $t = 5\ \text{s}$ to 80 m at $t = 15\ \text{s}$. Calculate the speed during this interval. [2]

$v = \frac{80 - 20}{15 - 5} = \frac{60}{10} = 6.0\ \text{m/s}$

Marking points: M1 for reading correct values or showing the gradient calculation. A1 for 6.0 m/s.

These marking points are for this original example and are not an official Cambridge mark scheme.

Common errors and how to correct them

• Confusing distance-time with speed-time graphs. On a distance-time graph, the gradient gives speed. On a speed-time graph, the gradient gives acceleration. Check the axis labels.
• Reading the total distance instead of the change. When calculating gradient, use the change in distance between two chosen points, not the total distance at one point.
• Thinking a curved section means constant speed. A curve on a distance-time graph means the speed is changing. Only a straight line shows constant speed.

How to apply this in an exam

When asked to find speed from a distance-time graph, draw a large gradient triangle on the graph. Use values from the triangle, not estimated values. Show the division clearly. A larger triangle gives a more accurate gradient.