Chapter 10.7, Problem 52AE

Catching a Bus Jodi’s bus leaves at 5:30 PM and accelerates at the rate of 3 meters per second per second. Jodi, who can run 5 meters per second, arrives at the bus station 2 seconds after the bus has left and runs for the bus.

a. Find parametric equations that model the motions of the bus and Jodi 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 Jodi will catch the bus. If so, when?

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