Two 455,000-lb locomotives pull 58 230,000-lb coal hoppers cars. The train starts from rest and accelerates uniformly to a speed of 32 mi/hr over a distance of 7000 ft on a level track. The constant rolling resistance of each car is 0.005 times its weight. Neglect all other retarding forces and assume that each locomotive contributes equally to the tractive force. Determine (a) the tractive force exerted by each locomotive at 16 mi/hr, (b) the power required from each locomotive at 16 mi/hr, (c) the power required from each locomotive as the train speed approaches 32 mi/hr, and (d) the power required from each locomotive if the train cruises at a steady 32 mi/hr.