After being forced out of farming, Lou has given up on trying to find work locally and is about to “ride the rails” to look for a job. Running at his maximum speed of 8 m/s, he is a distance d from the train when it begins to accelerate from rest at 1.0 m/s². 

(a) If d = 30 m and Lou keeps running, will he be able to jump into the train?

(b) Sketch the position function x(t) for the train, with x = 0 at t = 0. On the same graph, sketch x(t) for Lou for various distances d, including d = 30 m and the critical separation distance d_c, the distance at which he just catches the train. 

(c) For the situation d = d_c, what is the speed of the train when Lou catches it? What is the train’s average speed for the time interval between t = 0 and the moment Lou catches the train? What is the exact value of d_c?