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 1900 kg, was stopped at a red light when it was hit from behind by car A, of mass 1400 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 7.15 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 the car exceeding the speed limit of 35 mph?


For the speed of car A I tried the formula: (V_0)^2 = -2*g*mu*x where x is the distance traveled.

Plugging in my numbers I got: (2*9.8*0.650*7.15)^(1/2) = 9.544 m/s
and converting to mph: 21.35 mph
but this is not correct...

Explanation / Answer

car slides to a distance of 7.15m.
f =mg = 0.650 X (1400 + 1990) g  = 

f = (m1+m2)a

0.650 X (1400 + 1990)g = (1400+1900)a

a = 0.650g

v2 - u2 = 2as

0 - u2 = 2(- 0.650g)7.15

u = 9.55 m/s   just sfter collision

so in collison momentum will be conserved,

1900 X 0 + 1400 X v = (1400 + 1900) X 9.55 m/s

v = 22.51 m/s  = 22.51 X 60 X 60 / 1000 kmph  = 81.04 kmph

so it was exceeding with speed of (81.04 - 35) = 46.04 kmph

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