DistanceTime Graph
In order to study the motion of bodies, it is very useful to prepare the distancetime tables of their motion and draw the corresponding distancetime graphs.Â
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:Â
Distancetime table of the car 

Distance (in km) 
1 
2 
3 
4 
5 
6 
Time (in min) 
1.5 
3 
4.5 
6 
7.5 
9 
This is the distancetime 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}.
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The corresponding distancetime 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:
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Referring to the graph, we find thatÂ x_{1} is the position of car at time t_{1} and x_{2} is the position at time t_{2}. Therefore,
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Speed =
= = =
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Thus, v =
Notice, Î”x = AB and Î”t = BC and v = AB/BC
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Thus, to find the speed, we draw a triangle ABC and determineÂ Î”x/Î”t = AB/BC which is called the slope (or gradient) of the line. The slope of a straightline graph can be obtained by drawing a triangle anywhere on the line (irrespective of the size of the triangle) and calculatingÂ Î”x/Î”t. 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.Â
Thus, we conclude that:
1. If the distancetime graph of motion is a straightline, the motion is uniform.
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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 straightline 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.
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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 10^{5 }km/h 
Speed of light in vacuum 
1,080,000,000 km/h = 1.08 x 10^{9} km/h 