Question
Sun May 20, 2012 By:

Mon May 21, 2012
When the velocity of an object changes, we say that the object is accelerating. The change in the velocity could be due to change in its magnitude or the direction of the motion or both.

Let us consider an example of the motion of a body along a closed path. Fig (a) shows the path of an athlete along a rectangular track ABCD. Let us assume that the athlete runs at a uniform speed on the straight parts AB, BC, CD and DA of the track. In order to keep himself on track, he quickly changes his speed at the corners. It is clear that to move in a rectangular track once; he has to change his direction of motion four times.

Now, suppose instead of a rectangular track, the athlete is running along a hexagonal shaped path ABCDEF, as shown in Fig. (b). In this situation, the athlete will have to change his direction six times while he completes one round. If the track was not a hexagon but a regular octagon, with eight equal sides as shown by ABCDEFGH in Fig. (c), then he would have to change his direction eight times.

It is observed that as the number of sides of the track increases the athlete has to take turns more and more often. As we go on increasing the number of sides indefinitely, we will notice that the shape of the track approaches the shape of a circle and the length of each of the sides will decrease to a point. If the athlete moves with a velocity of constant magnitude along the circular path, the only change in his velocity is due to the change in the direction of motion which changes at each point.
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