You testify as an expert witness in a case involving an accident in which car A

Question

You testify as an expert witness in a case involving an accident in which car A slid into the rear of car B, which was stopped at a red light along a road headed down a hill (see the figure). You find that the slope of the hill is = 10.0°, that the cars were separated by distance d = 20.0 m when the driver of car A put the car into a slide (it lacked any automatic anti-brake-lock system), and that the speed of car A at the onset of braking was v0 = 19.0 m/s. With what speed did car A hit car B if the coefficient of kinetic friction was (a) 0.640 (dry road surface) and (b) 0.180 (road surface covered with wet leaves)?

Explanation / Answer

a) acceleration of the car, a = g*sin(10) - g*mue_k*cos(10)

= 9.8*sin(10) - 9.8*0.64*cos(10)

= -4.475 m/s^2

vo = 19 m/s

d = 20 m

vf = ?

Apply, vf^2 - vo^2 = 2*a*d

vf = sqrt(vo^2 + 2*a*d)

= sqrt(19^2 + 2*(-4.475)*19)

= 13.82 m/s

b)

acceleration of the car, a = g*sin(10) - g*mue_k*cos(10)

= 9.8*sin(10) - 9.8*0.18*cos(10)

= -0.035 m/s^2

vo = 19 m/s

d = 20 m

vf = ?

Apply, vf^2 - vo^2 = 2*a*d

vf = sqrt(vo^2 + 2*a*d)

= sqrt(19^2 + 2*(-0.035)*19)

= 18.96 m/s

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