Distance-time graph

The ability to draw graphs and to obtain information from them is one of the most important skills that a physicist needs to develop. You are also able to extract information more easily using graphs.

Example 1

A boy starts to walk at t = 0 s and walks from point A to point B a distance of 100 m for 10 s . He then stops and walk back towards his starting point in a time of 10 s.  The motion is as shown in fig 1.

 

Fig 1

If you use a table to present this information then it would be as follows:

time /s	Distance travelled /m
0	0
10	100
20	200

Table 1

After 10 s the boy has walked a distance of 100 m. And after 20 s the boy has walked a distance of 200 m( 100 m from A to B and another 100 m from point B to A).

Hence we can plot this on a graph as shown in fig 2 below.

Fig 2

As you can see from this graph the different coordinates will the give you the distance that the boy has walked after a particular time.

Now that you can plot the motion of an object on a graph. Let us see what you can do with a distance-time graph.

You would remember that the speed of an object is the rate of change of distance with time and that it can be calculated using the following equation

speed = distance travelled / time taken

With the distance-time graph the speed of an object at a particular time is the gradient of the line at that particular point.

Now what is the speed of he object at 5 s?

You will have to determine the gradient of the line at 5 s.

Hence the two coordinates that can be used are

(0,0)  and (10,100)

The gradient is thus

gradient = (y1 –y2)/(x1-x2)

                   = (0-100)/(0-10)

                   = –100/-10

                   10

Hence since the gradient a distance-time graph is the speed

speed at 5 s = 10 m/s