A vehicle of the following data is equipped with a 4-speed AT. The ratios are: 2.84(1 s), 1.60(2=), 1.0(3:d), 0.7(4th). The final drive ratio is 2.84. The torque converter has the characteristics as shown. The engine WOT output torque is also shown. The vehicle is being driven on level ground in the first gear with the torque converter unlocked. a) Present the differential equation system with the initial condition for the WOT performance simulation model of the vehicle in the first gear. Assume the vehicle is launched at engine idle RPM. b) Determine the engine angular acceleration and vehicle acceleration when the vehicle is just launched from stand still. c) Starting from time zero and using a step size of t=0.2, solve the differential equation system for one step, i.e., find the engine RPM and vehicle speed 0.2 second after launch. Vehicle Data Front axle weight: 1290 lbs Rear axle weight: 1240 lbs Center of gravity height: 18 inch Wheel base: 100 in. Air drag coefficient: 0.31 Frontal projected area: 20 square feet Tire radius: 10.0 in. Roll resistance coefficient: 0.02 Powertrain efficiency: 0.92 Mass moment of inertia of engine-impeller: 0.3 1bs.ft2