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. The position s at time t of an object having an acceleration a is s = ½ at².

(a) Find parametric equations that model the motions of the bus and Jodi as a function of time. 

(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).