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 1400 which crashed into stationary car B of mass 1000 . The driver of car A applied his brakes 10 before he skidded and crashed into car B. After the collision, car A slid 13 while car B slid 22 . The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.50.

Was the driver of car A exceeding the speed limit 55mph - (90km/hr ) before applying the brakes?

*The answer is actually no, but how do you go about proving this and finding the speed he was actually going at? * Please be clear and show the process of proving this.

Explanation / Answer

By conservation of energy;

dA = 13

Let v be the speed after collision.

.5*mA*vA^2=mA*g*µk*dA

vA=sqrt(2*g*µk*dA)

=sqrt(2*9.8*0.5*13)

vA=11.287 m/s
For B :
vB=sqrt(2*g*µk*dB)

=sqrt(2*9.8*0.5*22)

= 14.683 m/s

Velocity at the time of impact:

1400*vAi=1400*11.287+1000*14.683
vAi=21.775 m/s

Velocity while brake is applied:

.5*mA*V(A)^2=mA*g*µk*10+.5*mA*vAi^2
.5*V(A)^2=g*µk*10+.5*vAi^2
v(A)=sqrt(2*g*µk*10+vAi^2)
V(A) = 23.92 m/s

OR

86.112 km/hr

Thus, Driver is not crossing the speed limit.

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