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## Monday, January 25, 2010

### Types of distance-time graph

As we have seen in this post on distance-time graph, it is easier to extract information from a distance-time graph than from a paragraph or from a table of time and distance travelled.

We have seen in this post the gradient of the distance-time graph is the speed. Hence you must be able to deduce how the speed of an object varies according to the shape of its distance time graph.

Let us now look at some distance-time graph and see how the speed varies with time. We will then look at the corresponding speed-time graph for the object.

1. Fig 1 below shows a distance-time graph shows that the distance travelled by the object from time  0 s to t s  is 0 m. This means that the object has not moved at all and as a result it is motionless at the starting point.

The gradient of the graph is 0, hence it means that form time o s to time t s, the speed is 0 m/s.

The speed-time graph is thus as shown in fig 2.

Fig 1

Fig 2

2. Fig 3 below is a distance-time graph that shows an object whose distance travelled is constant form 0 s to time t s. We can thus assume that the object is stationary. The gradient of the graph is thus 0 which means that the speed is also  0 m/s from 0 s to t s. The speed-time graph would thus be as shown in fig 4 below.

Fig 3

Fig 4

3. Fig 5 below is a distance-time graph that shows an objects moving and the distance travelled is increasing.

The gradient of the graph is the speed. From the graph the gradient is a constant value but is not zero. Hence the speed-time graph is as shown in fig 6.

Fig 5

Fig 6

4. In fig 7 below we have a distance-time graph that shows an object that is moving as a result the distance travelled is increasing.

As we know the gradient of the graph is the speed and since the gradient is increasing then is it means that the speed is increasing. Hence the speed-time graph of the object is as shown in fig 8.

Fig  7

Fig 8