Catching a Train 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.
[Hint: The position s at time of an object having acceleration is ].
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).
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