Distance Time Graph For Uniform Motion
Distance Time Graph For Uniform Motion
The change in the position of an object with time can be plotted on the distance - time graph by choosing a scale best suited. To draw distance-time graph, time is plotted along X-axis and the distance of the body is plotted along Y-axis.
In this case, the slope of the distance-time graph is equal to the speed of the object.
Distance - Time graph for Uniform Motion
If an object travels equal distances in equal intervals of time, then it moves with uniform speed. For uniform speed, a distance- time graph represents a straight line.
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From the graph, it is clear that in equal interval of time 2s, the object covers equal distance 4m, so the motion is uniform and graph is a straight line. Calculation of speedTo calculate the speed of the object from a distance-time graph, we calculate the slope of the line. The slope is defined as the ratio of change in the value of y with the change in the value of x because the change in y represents the distance and change in x represents time. Ratio of distance with time represents speed. To find the change in x and y we choose any two points say A and B on the straight line. From points A and B, draw perpendicular AE and BC respectively, on time axis. the difference of the value represented by Point C and E represents a change in time.From points A draw perpendicular AD and BC. The difference of the value of distance at point B and D represents a change in distance. The distance traveled by the object from point A to B is = BC - DC = Time taken by the object to cover this distance = OC - OE = |
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ILLUSTRATION : The graph below shows the positions of a body at different times. Calculate the speed of the body as it moves from
(i) A to B, (ii) B to C and (iii) C to D.
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SOLUTION: (i) For the motion from point A to B, time taken, t= 4 -1 = 3 s Distance covered = 8 - 2 = 6 m (ii) For the motion from point B to C, time taken , t = 7 - 4 = 3 s Distance covered = 8 - 8 = 0 m (iii) For the motion from point C to D, time taken, t = 10 - 7 = 3 s Distance covered = 17 - 8 = 9 m |
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