Consider the following observation: The stopping distance for a car is much shorter than for a train going the same speed?. For the following questions, assume purely horizontal motion with the standard sign convention. i Assuming that the brakes of the train and the brakes of the car exert an equivalent stop- ping force magnitude, use the Impulse-Momentum Theorem, applied to each vehicle, to prove that the stopping time of the car is shorter than for the train. Hint: mc mT < 1. ii A shorter stopping time alone is not enough to prove a shorter stopping distance. We need more information about the nature of the motion of the train and car. Use Newton's 2nd Law, applied to each vehicle, to prove that the magnitude of the car's deceleration is greater than the magnitude of the train's deceleration. iii Using the facts that both the train and the car have the same initial velocity and that the magnitude of the train's deceleration is less than the magnitude of the car's deceleration, definitively prove that the stopping distance of the car is shorter than that of the train. Assume that the train and car have the same initial position. iv Determine which of the following graphs correctly depicts the position vs. time graph of the train and car as they come to a stop. Assume their initial positions to be 0 m. Briefly explain why the one you chose is correct and why the two that you did not choose are incorrect. Note: On the graphs below, to and ty are the stopping times of the car and the train, respectively. (A) Train t Car (B) Train (C) Train