1. A simplified model of a rear wheel drive vehicle accelerating from rest is shown in Figure 1. Gearbox W 59 Motor Tmotor F Twheel r q P We consider that the vehicle is powered by a PMG 132 drive motor that has a stall torque of t = 2406 lbf - in with a no-load speed of wn = 3590 RPM. 3000 Ts 2500 S Torque (in lbf) 2000 1500 1000 500 PMG 132 40 0 500 1000 1500 2000 2500 3000 3500 4000 Motor Speed (rpm) Wn -Torque -Power 5 35 30 25 20 15 10 Power (hp) The torque-speed curve of the electric motor is shown in Figure 2. The angular velocity of the motor is @motor. The power from the motor is transmitted to the wheels by a DANA H12 FNR gearbox. The gear box consists of a following gear train shown in Figure 3. Output Gear 4 Input Gear 3 Gear 1 Gear 2 Gear 1 has 24 teeth. Gear 2 has 72 teeth. Gear 3 has 24 teeth. Gear 4 has 106 teeth. The mass moment of inertia for each wheel is I = 1367 lbm-in. The radius of the drive wheel is r = 11 in. The angular velocity of the wheels is wwheel. The vehicle weighs W = 400 lbf. The acceleration of gravity is g = 386.2 in/s. (a) Derive the relationship between the torque on the rear wheel to its angular acceleration using the torque-speed curve of the motor, and Newton's laws applied to the vehicle. The equation should take the form