4.2 Motion graphs
Summary: How long does it take you to get to school? You can tell the story of a journey in a graph. Tags: science oxford-science student-book-7 physics Created: 2026-05-19 Last Updated: 2026-05-19
After this topic, you will be able to:
- interpret a distance-time graph
- use data from a distance-time graph to calculate average Speed.
Think back
- Give the equation for speed.
- State the différence between instantaneous and average speed.
- Estimate walking speed in m/s.
Key idea A distance-time graph shows a journey over time. We can take values for distance and time from the graph to calculate speed. Acceleration describes how quickly speed is changing.
Key words distance−time graph, acceleration
How long does it take you to get to school? You can tell the story of a journey in a graph.
What is a distance-time graph?
A distance-time graph is a useful way of showing how something moves. It shows the distance that something or someone travels over a certain time.
Figure 1 shows Lucia’s journey to school. The line shows how far she travelled each minute of the journey.
Figure 1A distance-time graph for Lucia’s journey to school. Full text alternative to the content
What does the graph tell us?
Figure 2 is a very simple distance-time graph. The object moves the same distance each second.
Figure 2A distance-time graphfor a constant (steady) speed. Full text alternative to the content
What happens if you stay still? Look at Figure 3. The line on the distance-time graph is horizontal.
Figure 3A distance-time graphfor a stationary (still) object. Full text alternative to the content
A State how you know that the speed in the graphs in Figures 1 and 2 is not changing.
The slope (gradient) of a distance-time graph tells you the speed. If the line is steep, the object is moving fast. If it is not very steep (shallow), the object is moving more slowly.
A car and a motorbike are driving down the same road at different but steady speeds. Figure 4 shows the distance-time graph for both vehicles. The line for the motorbike shows a faster speed and the line for the car shows a slower speed.
Figure 4A distance-time graph for two different speeds. Full text alternative to the content
B Suggest where you would draw a line on Figure 4 to show you walking to school at a steady speed.
What is acceleration?
When you are travelling, the speed changes during the journey.
If your speed is changing, you are accelerating. Accélération tells you how quickly your speed is changing (speeding up or slowing down). The slope (gradient) of the graph changes.
When you drop a ball, it gets faster and faster. It accelerates towards Earth. Figure 5 shows what happens. The distance-time graph in Figure 6 is curved. The distance-time graph is also curved if an object is slowing down.
Figure 5The ball accelerates.
Figure 6A distance-time graph for an accelerating object. Full text alternative to the content
C Write down whether the blue and red lines are showing average or instantaneous speeds.
How do you work out speed from a distance-time graph?
You can calculate speed from a distance-time graph. For example, in the first part of Lucia’s graph (see Figure 1), she walks 1000 m in 10 minutes or 600 seconds.
Stretch zone
- Copy and complete the sentences. A distance-time graph shows the direction/distance that an object travels in a certain direction/time. The colour/ gradient of the line tells you the speed. If the line is horizontal, the object is accelerating/stationary. If the line is an upward curve getting steeper, the speed of the object is decreasing/ increasing.
- Look at Figure 1. Calculate Lucia’s speed during the final 10 minutes of her journey.State the value of the speed in the horizontal parts of the graph.
Stretch zone
- Imagine two students travelling 3 km to school. One student walks and the other student travels by car. Describe and explain one similarity that there might be between the two graphs.Describe and explain one difference that there might be between the two graphs.