\fA car is stopped at a traffic light. The light turns green, and at time t = 0 the car starts moving and travels with a constant acceleration. At that instant a truck traveling at constant speed vt is alongside the car, with the front of each vehicle at position x = 0, as shown above. The truck passes the car, but the car later catches up to the truck in front of a house, such that at time to the front of each vehicle is at position x = D. a. On the axes below, sketch and label graphs of the velocity of the car and the velocity of the truck as a function of time. Indicate any important velocities or times. b. Two students are discussing how the speed of the car compares to the speed of the truck when both vehicles are in front of the house. Student 1 says, "The distance traveled by the car and the truck is the same, and the time is the same, so they must have the same speed." Student 2 says, "I don't see how that can be. The car catches up to the truck, so the car has to be going faster." i. Which aspects of Student 1's reasoning, if any, are correct? Support your answer in terms of relevant features of your graphs in part (a). ii. Which aspects of Student 2's reasoning, if any, are correct? Support your answer in terms of relevant features of your graphs in part (a). c. Derive an expression for the acceleration of the car. Express your answer in terms of D and vt d. Determine the time at which the speed of the car is equal to the speed vt of the truck. Express your answer in terms of to. Justify your