Given a vehicle with the following specifications:

Four wheel drive, front engine, high output 5.9-liter turbo Diesel, six-cylinder inline Weight: 3000 kg Wheelbase: 3.5 m Weight distribution (%f/r): 53/47 Centre of mass height: 1.0 m above the ground Max power: 305 bhp (227 kW) @ 2900 rpm Max torque: 555 lb-ft (752 Nm) @ 1400 rpm Redline: 3200 rpm Transmission: 6-sp. manual Ratios: 5.63:1, 3.38:1, 2.04:1, 1.39:1, 1.00:1, 0.73:1 Axle Ratio 4.10:1 Tires: 265/70R-17 Assume that the truck is equipped with a central differential in its drivetrain, i.e., the front and rear axles must transmit the same amount of torque, and that the tire’s coefficient of sliding friction is ???? = 0.8.

a) What is the maximum traction limited acceleration of the truck, if one assumes that front tire slip is the limiting factor? Ignore wind and rolling load in your calculation, giving some explanation of why this is

(or isn’t) reasonable. Does the front tire actually slip first? Hint: start with a free body diagram.

b) What is the maximum acceleration of the truck in first, second, and third gears? Can it reach the traction limit?

c) Judging by the choice of ratios that the design engineers have chosen for the transmission, comment on what you think was their objective in this choice.