In a proposed design for an electric automobile, the shaft of a four-pole three-phase induction motor is connected directly to the drive axle; in other words, there is no gear train. The outside diameter of the tires is 20 inches. Instead of a transmission, an electronic converter produces variable frequency three-phase ac from a 48-V battery. Assuming negligible slip, find the range of frequencies needed for speeds ranging from 5 to 70 mph. The vehicle, including batteries and occupants, has a mass of 1000 kg. The power efficiency of the dc-to-ac converter is 85 percent, and the power efficiency of the motor is 89 percent. Find the current taken from the battery as a function of time while accelerating from 0 to 40 mph uniformly (i.e., acceleration is constant) in 10 seconds. Neglect wind load and road friction.