The motion of the athlete along a circular path is considered an example of accelerated motion because, even though the magnitude of his velocity remains constant, there is a continuous change in the direction of his motion.
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As the number of sides increases, the length of each side of the track decreases to a point.
As the number of sides increases indefinitely, the shape of the track approaches the shape of a circle.
As the number of sides of the track increases, the athlete has to take turns more and more often.