A car of mass 1200 kg accelerates from rest to a speed of 8.0 m s⁻¹ in a time of 2.0 s.

a. Calculate the forward driving force acting on the car while it is accelerating. Assume that, at low speeds, all frictional forces are negligible.

b. At high speeds the resistive frictional force F produced by air on a body moving with velocity v is given by the equation F = bv², where b is a constant.
i. Derive the base units of force in the SI system.
ii. Determine the base units of b in the SI system.
iii. The car continues with the same forward driving force and accelerates until it reaches a top speed of 50 m s⁻¹. At this speed the resistive force is given by the equation F = bv². Determine the value of b for the car.
iv. Use your value for b in iii and the driving force calculated in part a to calculate the acceleration of the car when the speed is 30 m s⁻¹.
v. Sketch a graph showing how the value of F varies with v over the range 0 to 50 m s⁻¹. Use your graph to describe what happens to the acceleration of the car during this time.