Dynamics | Part IA, 2005

A car of mass MM travelling at speed UU 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 μ\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 14λu\frac{1}{4} \lambda u for each tyre, where λ\lambda is the drag coefficient and uu the instantaneous speed of the car. However, the tyres regain their dry-weather grip when the speed falls below 14U\frac{1}{4} U. Calculate the stopping distance and time under these conditions.

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