cie igcse · physics-0625 · 1.2 · v1

Motion

By the end of this page you can read distance–time and speed–time graphs, and calculate speed and acceleration from them.

Big question

How can a single graph tell the whole story of a journey?

01Speed is distance per unit time

Speed tells you how much distance an object covers each second: . Average speed uses the total distance travelled divided by the total time taken, even if the speed changed along the way.

02Two graphs, two stories

A distance–time graph shows where an object is; its gradient is the speed. A speed–time graph shows how fast the object is going; its gradient is the acceleration, and the area under the line is the distance travelled.

Two runners finish a 100 m course in the same 6 seconds. What do their distance–time graphs reveal about how they ran?

Constant speedt 3.3 ss 055 mv 16.7 m/s
Acceleratingt 3.3 ss 030 mv 18.3 m/s
FIG. 1 Both runners cover the same 100 m in the same 6 s, so their average speed is identical. The graphs expose the difference: a straight line means constant speed, while an upward curve means the gradient — the speed — is increasing. The red marker tracks each runner's position on the graph in real time.

Static description

The figure shows two runners on the same 100 m track above a shared distance–time graph. On the left, a runner moves at constant speed: the position dot advances evenly and the graph traces a straight line from the origin. On the right, a runner accelerates from rest: the dot starts slowly and speeds up, and the graph traces a curve that starts shallow and steepens. A vertical divider can be dragged to reveal more of either runner.

Constant speed. The runner covers equal distances in equal times. The distance–time graph is a straight line and the speed readout never changes.

Accelerating. The runner starts from rest and speeds up. The distance–time graph curves upward and the speed readout keeps rising.

What did you notice?

  • Both runners arrive at exactly when reaches — the average speed is the same.
  • The accelerating runner's curve starts shallow and steepens: the gradient (speed) grows.
  • The speed readouts in the figure never agree except near the crossover.

Worked example

A cyclist travels in at a steady rate. Find the speed, and say what the distance–time graph looks like.

  1. Write the equation you need: .
  2. Substitute the values with units: .
  3. State the shape of the distance–time graph for steady speed, and what its gradient means.
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Answer

. On a distance–time graph this is a straight line with gradient — the same number as the speed.