Description
Jake's driving a car at 20-m/s and sees a deer and slams on brakes to come to a stop.The coefficient of friction between tires and road as tires slide over the road is 0.55. How far will the car slide?
Explanation & Answer
Let the mass of the car be M, so the force due to weight is Mg, where g = 9.81m/s^2 = acceleration of gravity [although sometimes this is approximated as 10m/s^2]. Breaking force = coefficient of friction x weight = 0.55Mg. Acceleration of the car = - Breaking force / M = -0.55g.
If a body has acceleration a and initial speed u, then after displacement s has speed v, then v^2 = u^2 + 2as. When the car stops sliding v = 0, allowing calculation of the sliding distance s according to
0 = 20^2 + 2.(-0.55g).s = 400 - 10.79s, therefore s = 400/10.79 = 37.35m.
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