Beginning at time t = 0, a student pushes on a 30 kg crate, causing it to move at a constant velocity of 1.2 m/s toward an elevator door located 16 m away, as shown above. At t = 4.0 s, the elevator door opens and remains open for 5.0 s. The student immediately pushes harder on the crate causing the crate to accelerate uniformly towards the elevator door. The front of the crate reaches the elevator door just as it starts to close. a) How far is the crate from the elevator door at t = 4.0 s? b) Calculate the magnitude of the crate’s acceleration from the time the student began pushing harder on the crate until the front of the crate reached the front of the elevator door. c) Calculate the magnitude of the crate’s velocity the moment the front of the crate reached the front of the elevator door. d) On the axes below, sketch the graphs of the acceleration a, velocity v, and position x of the crate versus time between t = 0 and the time the front of the crate reaches the elevator.