1. An elevator is moving downward with a constant speed of 5 m/s for a period of 5s when an absent-minded passenger presses a button to go up to a higher floor. Suddenly, the tension in the cable of the elevator increases to 10,000 N and maintains this tension until the car and passenger have reached a speed of 2 m/s upward. At this point the elevator travels with this constant upward speed for an additional 10s. Note that the weight of the elevator and person together is 8000 N. For this problem, use g = 10 m/s^2 and set upward as the positive direction.

a. Determine the initial tension in the cable supporting the elevator when it is traveling 5 m/s downward.

b. Determine the magnitude of the acceleration of the elevator while the tension in the cable is 10,000 N.

c. Determine the time it takes for the elevator to change its velocity from the initial 5 m/s downward to the final 2 m/s upward.

d. The person on the elevator has a weight of 1000 N. On the graph below, create a graph to represent the normal force acting upon the person starting with the initial 5s interval of constant velocity downward. Continue your graph until the end of the 10s interval in which the elevator moved upward with a constant speed of 2 m/s.