You are called as an expert witness to analyze the following auto accident: Car

Question

You are called as an expert witness to analyze the following auto accident: Car B, of mass 2100 kg , was stopped at a red light when it was hit from behind by car A, of mass 1500 kg . The cars locked bumpers during the collision and slid to a stop. Measurements of the skid marks left by the tires showed them to be 7.25 m long, and inspection of the tire tread revealed that the coefficient of kinetic friction between the tires and the road was 0.650.

What was the speed of car A just before the collision?

By how many mph was car A exceeding the speed limit 35.0 mph ?

Explanation / Answer

change in kinetic energy = work

after the collision, both cars are stuck together and travel at a velocity V, the force of friction slows the cars down and eventually to a stop

KEf-KEi = -umgd
0- ( 0.5*3600 V²) = -0.65 * (2100+1500) * 9.8 * 7.25
V² = 92.365
V = 9.610 m/s

that is their velocity after the collision

momentum is conserved so

m1v1 + m2v2 = (m1+m2)V
(1500)v1 + (2100)(0) = (3600)(9.610)
v1 = 21.665m/s

b.
convert 21.665 m/s to mph

21.665m/s x 3600s/hr = 77994 m/hr

77994m/hr x 1mi/1069m = 72.95 mi/hr

72.95 - 35 = 37.95 mph

so answer is 37.95mph over the limit

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