Consider a car with length l, and choose the origin in its rest frame such that the front of the car is at XF 0, and the rear of the car is at xr = l. = a) Move to an inertial frame with coordinates x', t' where the car is moving to the left with constant velocity v. Find an equation relating x and t (the worldline of the front of the car in this frame), and another equation relating x' and 'R (the worldline of the back of the car in this frame). R b) Use your results from the previous part to obtain the length of the car in the primed frame in terms of l (that is, rederive length contraction from your results). Also, what is the slope of the two worldlines in the spacetime diagram with ct' the vertical axis and x' the horizontal axis? = c) The car has a resting length of l 5 m, a rest mass of 2000 kg, and in the primed frame is moving at 3c/5. Find the energy and momentum of the car in its rest frame, and the energy, momentum and length of the car in the moving frame. (The speed of light is 3 108 m/s.)