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Distance-Time Graphs — AQA GCSE Combined Science Trilogy 8464 - Physics Revision Notes & Topical Questions

5 min read 8 parts Lesson 25 of 44

📚 AQA GCSE Combined Science Trilogy 8464 - Physics Hub / Topical Revision
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Section 1 of 8What a distance-time graph shows

A distance-time graph shows how far an object is from a starting point at each moment. Time is plotted along the horizontal axis (x-axis) and distance along the vertical axis (y-axis). Because the graph tells us the position at every moment, we can read off where the object is, when it moves, when it stops and how fast it goes.

Distance in these graphs is measured in metres (m) or kilometres (km) and time in seconds (s) or hours (h). Always check the axis labels and units before reading values, and note where each axis begins, since the graph might not start at zero.

Section 2 of 8The meaning of the shape

The shape of the line tells the story of the journey:

1Horizontal line
a horizontal line means that the distance is not changing, so the object is stationary;
2Straight sloping line
a straight sloping line means that the distance is changing at a steady rate, so the object moves at a constant speed;
3Steeper
a steeper straight line means a higher speed;
4Curves upwards
a line that curves upwards (getting steeper) means that the object is speeding up (accelerating);
5Curves towards the horizontal
a line that curves towards the horizontal (getting flatter) means that the object is slowing down;
6Downwards
a line that slopes downwards shows that the distance from the start is falling, so the object is coming back towards the start.

Note that a downward-sloping line does not mean a negative speed. Speed is the size of the rate of change, so the speed is still the numerical value of the gradient, without the minus sign. It is the direction that changed.

Section 3 of 8Finding speed from the gradient

The gradient (slope) of a distance-time graph is equal to the speed:

gradient = change in distance ÷ change in time = speed

To find the gradient of a straight line, draw a right-angled triangle against the line, as large as is practical.

Finding speed from the gradient
Read the vertical side (the change in distance) and the horizontal side (the change in time), then divide.
Use points that are well separated and lie on gridlines to improve accuracy.
The units of the gradient are the units of distance divided by the units of time, for example m/s.

For a curved graph, the speed at a particular moment is the gradient of the tangent, a straight line drawn to just touch the curve at that point. This is called the instantaneous speed.

Section 4 of 8Average speed from the graph

The average speed over the whole journey is the total distance travelled divided by the total time, not the average of the speeds.

1
Suppose a runner goes 400 m in 100 s and then rests for 100 s.
2
The average speed over the whole 200 s is 400 ÷ 200 = 2.0 m/s, though the runner was moving at 4.0 m/s while running.
3
Rest periods lower the average.
4
On the graph, the average speed is the gradient of the straight line joining the start and finish of the journey.

This topic leads directly to the definition of speed in 1.1.2, and the corresponding graph of velocity against time in 1.1.5.

Section 5 of 8Worked reading of a graph

Suppose a graph for a bus shows these stages: 0 to 40 s, a line rising from 0 m to 200 m; 40 to 70 s, a horizontal line at 200 m; 70 to 100 s, a line rising to 500 m.

1
In the first stage, the speed is 200 ÷ 40 = 5.0 m/s.
2
In the second stage, the bus is stationary at a stop.
3
In the third stage, the bus covers 300 m in 30 s, which is 10 m/s, so it is faster.
4
Notice that the third line is steeper than the first, which agrees with its larger speed.
5
When describing a graph in an exam, quote values with units from the axes to support what you say,
  • as in 'the bus is stationary between 40 s and 70 s because the distance stays at 200 m'.

Also check carefully whether a graph shows distance from the start or total distance travelled: a returning journey only appears as a falling line on the first.

Section 6 of 8Worked examples

  1. A cyclist's graph is a straight line from (0 s, 0 m) to (20 s, 100 m). Find her speed.

  2. A graph shows a car moving 60 m in the first 10 s, staying at rest from 10 s to 25 s and then travelling a further 90 m between 25 s and 40 s. Find its speed in each part and the average speed for the whole journey.

  3. A distance-time graph for a walker is a line from (0 s, 0 m) to (50 s, 60 m), and then a line from (50 s, 60 m) to (110 s, 0 m). Describe the motion and find the speeds.

Section 7 of 8Key terms

TermMeaning
GradientChange in vertical value divided by change in horizontal value.
StationaryNot moving; shown by a horizontal line on a distance-time graph.
Constant speedEqual distances in equal times; shown by a straight sloping line.
Average speedTotal distance divided by total time.
TangentA straight line touching a curve at one point; its gradient is the speed at that instant.

Section 8 of 8Exam technique

1
Thinking that a horizontal line means constant speed. It means that the object is at rest.
2
Thinking that a distance-time graph shows the path taken. It shows the distance against time, not the shape of the route.
3
Confusing a downward slope with going slower. It means returning, at a speed given by the size of the gradient.
4
Reading the gradient with units wrong, such as dividing time by distance.
5
Taking the average of the speeds for a journey with different speeds, rather than total distance divided by total time.

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