A small experimental vehicle has a total weight W of 1225 lb including wheels and driver. Each of the four wheels has a weight of 85 lb and a centroidal radius of gyration of 20 in. Total frictional resistance R to motion is 94 lb and is measured by towing the vehicle at a constant speed on a level road with engine disengaged. Determine the power output of the engine for a speed of 35 mi/hr up the 13-percent grade (a) with zero acceleration and (b) with an acceleration of 8 ft/sec2. (Hint: Power equals the time rate of increase of the total energy of the vehicle plus the rate at which frictional work is overcome.)