A car of mass m is moving with speed v on a level road. The coefficient of static friction between the tyres and the dry road surface is μs=0.50. When the driver applies the brakes, the wheels continue to roll without slipping until the car stops.
a. (i) Derive an expression for the minimum stopping distance Smin of the car in terms of v, g and μs.
b. (ii) Using your expression, find the ratio of minimum stopping distances for the same speed v on a wet road where μs=0.20 to that on the dry road.
c. (iii) Suppose the driver brakes so hard that the wheels lock and slide on the dry road, for which the coefficient of kinetic friction is μk=0.30. Calculate the percentage increase in stopping distance compared with the value obtained in part (i).