A vehicle of the following data is equipped with a 4-speed AT. The ratios are: 2.84(1st), 1.60(2nd), 1.0(3rd), 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 Center of gravity height: 18 inch Air drag coefficient: 0.31 Tire radius: 10.0 in. Powertrain efficiency: 0.92 Torque 250 (ft.lb) 200 150 100 50 0 torque 1000 2000 Rear axle weight: 1240 lbs Wheel base: 100 in. Frontal projected area: 20 square feet Roll resistance coefficient: 0.02 Mass moment of inertia of engine-impeller: 0.3 lbs.ft² Max. Torque Max Power 3000 4000 5000 6000 237.5 (HP) 190 95 7000 142.5 Power 47.5 Max. Power: 200 нрат 5500 Rem 'Mex, тогдые: 199 ft.bat 3850RPM RPM/n100 50 TORQUE RATIO 0 2.2 2.0 1.8 1.6 1.4 1.2 1.0 .8 1000 K CAPACITY FACTOR 300 280 260 240 220 200 180 160 140 120 100 80 60 40 20 0 2000 3000 TORQUE RATIO 4000 5000 6000 IMPELLER SPEED- EFFICIENCY- PERFORMANCE BASED ON 200 LB. FT. CONSTANT INPUT TORQUE SPEED RATIO 7000 100 .9 1.0 90 80 70 60 50 40 30 20 10 0 EFFICIENCY - PERCENT 95 47.5 RPM 3200 3000 2800 2600 2400 2200 2000 1800 1600 1400 1200 1000 800 600 400 200 199 ft.bat 3850RPM 0 IMPELLER SPEED - RPM