Using Matlab,

The acceleration of a car is given by the following formula that includes an acceleration term A due to the engine torque and an air drag term that is proportional to the square of the velocity: dv/dt = A-C middot v^2 It is desired to measure the 0-60 mph performance of the car, as well as its braking performance from 60-0 mph. To this end, the driver first applies maximnm torque until the car reaches 60 mph and measures the cufrcs|iondiug time, say, t_60, and then, she applies the brakes until the car stops, and measures the stopping time, t_stop. Let us discretize the time as, t_n = (n - 1)T, where n = 1, 2, 3,...,and T = 0.001 sec is a small time step. Then, the above differential equation may be replaced by the following difference equation: u(n + 1) = v(n) + T middot [A(n) - C middot v^2(n)] (3) where v(n) is iu units of mph. the drag constant is chosen as C = 0.008, and the initial acceleration and sulsequent braking action can be modeled by: A(n) = {30, if t_n lessthanorequalto t_theta0 -2, if t_60