A race: A man enters a race that involves running and swimming. He lines up at the starting gate and begins running very fast, hoping to take the initial lead before settling into a constant, slower...

A race: A man enters a race that involves running and swimming. He lines up at the starting gate and begins running very fast, hoping to take the initial lead before settling into a constant, slower pace for a distance run. To complete the race, he must swim across a river and back before running back to the starting gate. He swims at a constant rate but cannot swim as fast as he runs. Let S = S(t) denote the distance of the contestant from the starting gate.

a. Make a graph of S versus t. Note on your graph the places where you know that S is linear.

b. Make a graph of the contestant’s velocity. c. Make a graph of the contestant’s acceleration.