In the system, the total mass of the vehicle is 4000kg, the moment of inertia of the vehicle around c.g. is J = mr- (r = 0.64m-), 1= 1.4m, and 12 = 0.9m, friction coefficient c for each tire- and-wheel assembling is 2000N*s/m. The steps in the design and simulation process should include (but would not be limited to): (1) Draw the simplified physical model for the vehicle based on the above assumptions. (2) Develop a mathematical model using the simplified physical model. a. Draw the free-body diagram of the vehicle and write differential equations, input- output equations or state variable equations for the system. b. The input is the impulse moment by the engine being shut off and the outputs are the rotation and up-and-down motion in the x direction