A motor-car of mass 1000kg is travelling on a level, rough road at 20ms−1 when the driver suddenly applies the brakes so that the wheels lock and the tyres slide.
a. (i) Derive an expression for the stopping distance s of the car in terms of the initial speed v0, the coefficient of kinetic friction μk between tyres and road, and g.
b. (ii) If μk=0.30, calculate the distance in which the car comes to rest and also find the total work done by friction during this process.