Chapter 9, Problem 42RE

Uniform Motion Mary’s train leaves at 7:15 AM and accelerates at the rate of 3 meters per second per second. Mary, who can run 6 meters per second, arrives at the train station 2 seconds after the train has left.

(a) Find parametric equations that model the motion of the train and Mary 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 Mary will catch the train. If so, when?

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