# Representing journeys

## Key points

• A journey describes the motion of an object over time.

• A journey can be represented using a distance-time graph.

• The graph will show when an object is moving and when it is stationary.

• The graph can also be used to calculate how fast the object is travelling.

## Distance-time graphs

What is a distance-time graph?

A is a useful way to represent the motion of an object. It shows how the distance moved from a starting point changes over time.

Time in seconds is on the x-axis. Distance in metres is on the y-axis.

How to interpret a distance-time graph

Have a look at this graph.

At a, the object is travelling at a , so it is shown with a straight diagonal line, where the of the line tells you the speed.

At b, the object is so it is shown with a curved line which gets steeper.

At c, the object is travelling at a constant speed again, but this time it is faster, so the straight line is steeper - it has a larger gradient.

At d, the object is , so line is curved and gets less steep.

At e, the object is , so its distance does not change as the time taken increases. This means that for a stationary object, the line is flat and the gradient (the speed) is zero.

## Calculating speed from a distance-time graph

The gradient of the line on a distance-time graph is equal to the speed.

Calculate the gradient of the line using the following equation:

$$gradient = \frac {change~in~y~value}{change~in~x~value}$$

When the speed is calculated from a distance-time graph, the units for speed will depend on the units used for the y axis (distance) and the units used for the x axis (time taken).

For example, if the distance is in m (metres), and the time is in s (seconds), then the calculation involves:

m ÷ s

and the units will be m/s.

If the distance is in km (kilometres), and the time is in h (hours), then the calculation involves:

km ÷ h

and the units will be km/h.

In the units for speed, the / symbol means the same as the ÷ symbol.

Calculate the speed of the object represented by the green line in the graph, from 0 to 4 s.

change in distance = (8 - 0) = 8 m

change in time = (4 - 0) = 4 s

$$speed = \frac {distance}{time}$$

$$speed = 8 ÷ 4$$

$$Speed = 2 m / s$$

## Calculating average speed from a distance-time graph

Watch Brian Cox explain how to calculate average speed using a distance-time graph.

## Test yourself

The distance-time graph graph below represents a car's journey. Have a look at the graph and answer the following questions:

1. At which part of the journey was the car stationary?

2. At what point in the journey was the car travelling the fastest?

3. What is the total distance travelled by the car?

4. How far did the car travel between 2 seconds and 3 seconds?

5. Calculate the speed of the car between 2 seconds and 3 seconds.

1. C

2. B

3. 6 metres

4. At 2 seconds the car had travelled 1 m and by 3 seconds it had travelled 4 m.

4 - 1 = 3.

The car travelled 3 m between 2 seconds and 3 seconds.

1. The car travelled 3 m between 2 seconds and 3 seconds.

3 ÷ 1 = 3

The speed of the car between 2 seconds and 3 seconds was 3 m/s.