Reading a distance-time graph

Representing motion

A distance-time graph plots time t on the horizontal axis (x-axis) and distance covered d on the vertical axis (y-axis). It allows you to visualize how an object moves.

Uniform motion

If the object moves at constant speed (uniform motion), the graph is a straight line. The slope of this line is precisely the speed:

slope = change in d / change in t = v

The steeper the line (the greater the slope), the higher the speed. A horizontal line means the object is stationary (v = 0).

Non-uniform motion

If the speed changes over time, the curve is no longer a straight line but bends. The instantaneous speed at a given instant then corresponds to the slope of the tangent to the curve at that precise point.

Worked example

Time (s)	Distance (m)
0	0
2	10
4	20
6	30

Between each point, the distance increases by 10 m every 2 s, i.e. v = 10/2 = 5 m/s: the motion is uniform, the line is perfectly straight.

Classic pitfall

Do not confuse a straight line with a steep slope (high speed) with a curve that rises sharply at one point (acceleration, varying instantaneous speed). Always check whether the points line up on a straight line or not before concluding that the speed is constant.