IGCSE Physics / Movement and position
Distance-time graphs
Edexcel International GCSE Physics (4PH1), chapter 1: Movement and position, specification point 1.3, M4A, M4E. Free lesson.
Read the revision notes · IGCSE Physics past papers
A distance-time graph shows how an object's distance from its starting point changes over time. Its shape tells you whether the object is stationary, moving at a constant speed or speeding up, and its gradient can be used to find speed.
What the shape of a distance-time graph means
Time is shown along the bottom axis and distance from the start up the side. The shape of the line shows how the motion changes. A straight sloping line means the object travels the same distance each second, so it moves at a constant speed. A horizontal line means its distance is not changing, so it is stationary. A steeper slope means a greater speed. A student walks to a bus stop, waits, then runs for the bus. On a distance-time graph, a flat section means stopped, not moving at a steady speed.
How to find speed from a straight line
The gradient is the steepness of a line. On a distance-time graph, gradient gives speed because it compares how far the object travels with how long it takes. Use a large triangle that fits along the straight section, then read its rise and run from the axes, including their units. Gradient = distance up ÷ time across. Speed is measured in metres per second (m/s).
How to describe a journey using the graph
A description should include figures read from the axes, with units. This makes it clear how far the object travelled and how long each part of the journey lasted. For example, give the distance and time for the walk, say when the object stopped, then give the distance and time for the run.
How to plot a distance-time graph
When plotting readings, label each axis with the quantity and unit. Choose a clear scale, plot each reading carefully, then join the points according to their pattern. If the points curve, the curve should be smooth because the motion changes continuously between readings. Choose a scale that increases in ones, twos or fives. Mark each reading to within half a small square. Use one smooth curve for curved points, or one ruled straight line if the points lie on a straight line. Do not join the points dot to dot.
How to find speed at one moment on a curve
A curve means the speed is changing, so its gradient is different at different moments. To find the speed at one moment, draw a tangent: a straight line that touches the curve at that point and matches its slope. Find the gradient of the tangent using a large triangle. A line joining two points on the curve gives average speed, not the speed at one moment. If a distance-time curve gets steeper, its gradient and speed are increasing.
How to explain that an object is speeding up
A two-mark explanation links the shape of the line to what gradient means. If the line curves and gets steeper, its gradient is increasing. Since gradient is speed, the object is speeding up. State that the line curves and gets steeper. Link the steeper gradient to increasing speed.