Chapter 10.7, Problem 51AE

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 $t$ of an object having acceleration $a$ is $s=\frac{1}{2}a{t}^2$].

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).