In: Physics
In the television show “The Six Million Dollar Man”, Colonel Austin had superhuman powers. In one episode, he tries to catch a man fleeing in a sports car. We’ll assume in this problem that the distance between them at t=0 is 100 m. The car starts at rest. At t = 0.0 s, the driver notices Colonel Austin. From then on, the car accelerates at 5.0 m s -2 , away from Austin. Sweet, but a bit slow on the uptake, Colonel Austin remains motionless until t = 2.0 s, at which point he begins his pursuit, at a constant speed of 50 m/s. a) How far ahead is the car when Colonel Austin begins to move? b) At what time (t>0) is Austin furthest ahead of the car? And what is that separation? c) At what time(s) does Austin catch the car? d) What is the critical initial separation (all other parameters remaining the same) beyond which Colonel Austin will never catch the car?