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. 

The position s at time t of an object having acceleration a is s = 1/2at².

(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).