A car of mass $M$ travelling at speed $U$ on a smooth, horizontal road attempts an emergency stop. The car skids in a straight line with none of its wheels able to rotate.

Calculate the stopping distance and time on a dry road where the dry friction coefficient between the tyres and the road is $\mu$.

At high speed on a wet road the grip of each of the four tyres changes from dry friction to a lubricated drag equal to $\frac{1}{4} \lambda u$ for each tyre, where $\lambda$ is the drag coefficient and $u$ the instantaneous speed of the car. However, the tyres regain their dry-weather grip when the speed falls below $\frac{1}{4} U$. Calculate the stopping distance and time under these conditions.