A car is traveling on a level road with speed v0 at the instant when the brakes

Question

A car is traveling on a level road with speed v0 at the instant when the brakes lock, so that the tires slide rather than roll.

Part A

Use the work-energy theorem to calculate the minimum stopping distance of the car in terms of v0, g, and the coefficient of kinetic friction ?kbetween the tires and the road

Part B

By what factor would the minimum stopping distance change if the coefficient of kinetic friction were doubled ?

Part C

By what factor would the minimum stopping distance change if the initial speed were doubled?

Part D

By what factor would the minimum stopping distance change if both the coefficient of kinetic friction and the initial speed were doubled?

Explanation / Answer

Part A:

From work energy theorm, 0.5mvo2 = Fs

   s = (0.5mvo2)/F

      = (0.5mvo2)/Ukmg

   s = vo2/2Ukg

     =

PART B:

s' = vo2/2(2Uk)g

   = s/2

Hence, the distance travelled is reduced by half

Part C:

s = vo2/2Ukg

= (2vo)2/2Ukg

s'= 4(vo2/2Ukg )

s' = 4s

The distance is increased by 4 times.

Part D:

s' = (2vo)2/2(2Uk)g

    = 2(vo2/(2Uk)g )

s' = 2s

The distance is increase by two times.

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