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Sketch a distance-time graph for a body moving with variable speed? 

Difficulty: Medium

An object moving with variable speed:

When an object does not cover equal distances in equal intervals of time then its speed is not constant. In this case, the distance-time graph is not a straight line as shown in the figure. The slope of the curve at any point can be found from the slope of the tangent at that point. For example.

The slope of the tangent at P= $\frac{RS}{QS} = \frac{30m}{10s} = 3m/s$

Thus, the speed of the object at P is 3 ms-1

Note:

The speed is higher at instants when the slope is greater, speed is zero at instants when the slope is horizontal.

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