You\'re driving along a rural highway in a light rain at 62 mph (28 m/s). As you

Question

You're driving along a rural highway in a light rain at 62 mph (28 m/s). As you round a bend, you see a 30-mph (13 m/s) speed zone ahead, with a police car parked just beyond the sign. You quickly estimate that the sign is about 100 m from you. You know that the coefficient of static friction between your car's tires and the wet road is 0.26, the coefficient of kinetic friction is 0.20, the car's mass is 1280 kg, and that the average force of air resistance acting on the car at these speeds is 1100 N.

Question:If you brake as hard as you can without going into a skid, can you slow down to the speed limit before you reach the speed zone?

Need to start with N2L and go from there

Explanation / Answer

If we avoid skidding that means we will rely solely on kinetic friction.

Thus in this case at max strength of kinetic friction,
Opposing force = 0.2*1280*9.8 + 1100 = 3608.8 N
Thus acceleration = -3608.8/1280 = - 2.819375 m/sec2

Now using v2 = u2+2as
v = (282-2*2.819375*100) = 15.5 m/sec.

Thus we cannot slow down without skidding

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