You have been hired as an expert witness in a court case involving an automobile

Question

You have been hired as an expert witness in a court case involving an automobile accident. The accident involved car A of mass 1430 kg which crashed into stationary car D of mass 1110 kg. The driver of car A applied his brakes 15 m before he skidded and crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Part A Show that the driver of car A was exceeding the 55-mi/h (90 km/h) speed limit before applying the brakes. Find this speed.

Explanation / Answer

part A

fromm momentum conservation

momentum before collision = momentum after collision

mA*vA = v*(mA+mB)

1430 *vA = v*(1430+1110)

v = 0.58*vA

car A

initial KE = (1/2)*mA*vA^2

work done by frcition Wf = -uk*(mA+mB*g)*x2 - uk*mA*g*x1

final KE = (1/2)*(mA+mB)*v^2

from work energy theorem

-uk*(mA+mB)*g*18 - uk*mA*g*15 = (1/2)*(mA+mB)*v^2 - (1/2)*mA*vA^2

-(0.5*(1430+1110)*9.8*18) - (0.5*1430*9.8*15) = (1/2)*(1430+1110)*0.58^2*vA^2 - (1/2)*1430*vA^2

vA = 33.81 m/s = 121.72 km/h = 75.73 mi/h <<<<<==============ANSWER

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