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Distance-Time Graph

In order to study the motion of bodies, it is very useful to prepare the distance-time tables of their motion and draw the corresponding distance-time graphs.

Suppose a car is travelling on a straight road with a constant speed, which is indicated by the speedometer of the car. The driver measures the time the car takes to pass every successive kilometre stone on the side of the road. He finds that the car passes the first kilometre in 1 1/2 min, the second kilometre in 3 min and so on. Thus, he notes the position of the car every one and a half minutes. He prepares the table of his

observation as follows: 

Distance-time table of the car

Distance (in km)







Time (in min)







This is the distance-time table of the motion of the car. It gives the position of the car at some instants of time, namely 1.5 min, 3 min, 4.5 min, 6 min, 7.5 min, and 9 min. It does not give the position of the car at other times such as 2 min, 4 min, etc. Thus, the table gives only limited information about the motion of the car. The table reveals that the car travels 1km every 1.5 min, i.e. the speed of the car 1 km/1.5 min or 2/3 km per minute or 2/3 x 60 = 40 km per hour, which is written as 40 km/h or 40 km h-1.

The corresponding distance-time graph of the motion gives more information.

The graph is a straight line, which indicates that the motion of the car is uniform. Further, from the graph we can find the position of the car at any instant of time. Finally, the graph can also be used to determine the speed of the car.

This is done as follows:


Referring to the graph, we find that x1 is the position of car at time t1 and x2 is the position at time t2. Therefore,


Speed =

= = =


Thus, v =

Notice, Δx = AB and Δt = BC and v = AB/BC

Thus, to find the speed, we draw a triangle ABC and determine Δx/Δt = AB/BC which is called the slope (or gradient) of the line. The slope of a straight-line graph can be obtained by drawing a triangle anywhere on the line (irrespective of the size of the triangle) and calculating Δx/Δt. The value of the slope calculated from triangles ABC or PQR is the same. The slope of the graph comes out to be 40 km/h, which is the speed of the car. 

Thus, we conclude that:

1. If the distance-time graph of motion is a straight-line, the motion is uniform.

Example : The moving body covers equal distances in equal intervals of time, however small the time interval may be.

2. The slope of the graph gives the speed of the body, and

3. The slope of the straight-line graph is the same, irrespective of the length of the time interval chosen.

The following table gives the measured value of the speeds of some common moving bodies.

Speeds of some common bodies

Average speed of a snail

0.02 km/h

Average speed of a tortoise

0.5 km/h

Average speed of a fast athlete in a 100 m race

36 km/h

Maximum speed of a deer

85 km/h

Maximum speed of the world's fastest train

255 km/h

Wind speed in a light breeze

30 km/h

Speed at which earth goes round the sun

107,000 km/h = 1.07 x 105 km/h

Speed of light in vacuum

1,080,000,000 km/h = 1.08 x 109 km/h

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