Bill’s train leaves at 8:06 AM and accelerates at the rate of 2 meters per second per second. Bill, who can run 5 meters per second, arrives at the train station 5 seconds after the train has left and runs for the train. 

(a) Find parametric equations that model the motions of the train and Bill as a function of time. The position s at time t of an object having acceleration a is s = ½ at².

(b) Determine algebraically whether Bill will catch the train. If so, when? 

(c) Simulate the motion of the train and Bill by simultaneously graphing the equations found in part (a).