Question

A 1000 kg car is driving at a speed of 35 m/s on flat level ground. A road hazard ahead causes the driver to slam on the brakes, and the tires start to skid. a) If the pavement is dry (and thus μk = 0.7) how far will they travel before coming to a stop? b) If the pavement is wet, μk is reduced to 0.3. Now how far would they travel before coming to a stop?

Answer 1

a)

μ_k = coefficient of kinetic friction = 0.7

a = acceleration due to frictional force = - μ_k g = - (0.7) (9.8) = - 6.86 m/s²

v_i = initial velocity of the car = 35 m/s

v_f = final velocity of car = 0 m/s

d = stopping distance = ?

using the equation

v²_f = v_i² + 2 a d

0² = 35² + 2 (- 6.86) d

d = 89.3 m

b)

μ_k = coefficient of kinetic friction = 0.3

a = acceleration due to frictional force = - μ_k g = - (0.3) (9.8) = - 2.94 m/s²

v_i = initial velocity of the car = 35 m/s

v_f = final velocity of car = 0 m/s

d = stopping distance = ?

using the equation

v²_f = v_i² + 2 a d

0² = 35² + 2 (- 2.94) d

d = 209.33 m