Answer Happy

3.) Realistic Drag Force (18 pts.) Consider a sports car (total mass m) on a horizontal road. Neglect friction but include an airdrag force, Fa = - Byv?, depending on the speed, v, of the car, and B2 = CpA with C: drag coefficient, p: air density, A: effective cross sectional area of the car. The car engine is capable of producing a maximum power Po. (a) Use Newton's 2. law of motion and the definition of power, P = dE/dt, to rewrite the net acceleration as a function of P. In the absence of drag, solve this equation analytically for v(t) and sketch the solution in a graph. (b) Use a first-order difference method to discretize the equation derived in (a) and express the speed at time step i in terms of the previous time step i – 1. Sketch the numerical solutions for the speed in a graph for both a large and a (not too) small initial speed, vo. (c) What is the terminal speed of the car for C=0.35, A=1.5m², p=1.29m3, Po=150kW?