To pull a car up the inclined bed of a tow truck, the driver attached a steel cable to the car. The other end of the cable is wrapped around a steel cylinder, which is rotated by an electric motor. This pulls the cable and hence the car up the inclined bed. Consider the bottom of the ramp to be point A, and a point that is at the top of the ramp to be point B. The car is stationary at point A, and should again be stationary at point B. So the car must have some acceleration in the beginning to cause it to start moving upwards, then after it reaches some point C (somewhere in-between A and B), the force pulling it up is stopped, and the car keeps going up by its inertia, and slows down to a stop at B due to gaining height and due to friction. The acceleration from A to C may be assumed to have a constant value (hence a constant force). The objective is to find the shortest possible time to go from A to B, without exceeding the following condition: The cable must not stretch by more than a certain percent of its length at any point. To solve this problem, calculate the following:

a. The maximum force that you can apply, based on the Young’s Modulus.
b. The torque applied by the electric motor placed at the top of the ramp (during motion from A to C).
c. The acceleration that this force creates.
d. The point C up to which you need to apply this force. At this point the force goes to zero, and the car coasts to a stop at point B.
e. The time it takes to cover A to C, and C to B, and the total time A to B.