The all-wheel drive car shown in Figure 2 is at rest on a level road. The car's mass centre is at G. The car starts moving with an initial acceleration. For this car: (a) Draw the free body diagram showing all the forces acting on the car. (b) Assuming the coefficient of static friction between the tyres and the track is , for front tyres, and uz for rear tyres, obtain an expression for the maximum possible initial acceleration that can be achieved by the car (amar) without having any of the wheels slip on the track. Neglect the mass of the wheels. (c) Design part (using MATLAB): You have two types of tyres, type A with the coefficient of static friction of a = friction of uB = 0.84. Assuming h = and type B with the coefficient of static cm and l, + l2 = cm, discuss in detail which type should be used for front 1.15 45 260 wheels and which one for the rear wheels to achieve the highest maximum initial acceleration. Develop a complete design, considering all possible cases, and by varying l1 or l2 as a parameter and monitoring/plotting amax. Explain each part clearly and come up with a final optimum design considering realistic values for l1 and l2. G l2 4 Figure 2