You are the juror of a case involving a drunken driver whose 962kg sports car ra

Question

You are the juror of a case involving a drunken driver whose 962kg sports car ran into a stationary 2013kg station wagon stopped at a red traffic light. The cars stuck together and slid with locked wheels for 11m before coming to rest. The coefficient of sliding friction on the dry road was 0.6. a) Estimate the speed of the sports car when it hit the station wagon. b) Estimate the instantaneous acceleration of the sports car during the actual collision if the colliding cars reach the same final speed after collapsing a combined total distance of 0.7m.  

Explanation / Answer

mass of the driver m = 962 kg mass of station wagon m1= 2013 kg the cars slide for S = 11 m before coming to rest The coefficient of sliding friction on the dry road wask= 0.6 a)Applying the law of conservation of momentum m * u + m1 * u1 = (m + m1) * v u is speed of the sports car when it hit the station wagon,u1=0 (intial speed of station wagon) and v is the combined speed ofthe cars after collision and is equal to (2* k * g * S)^(1/2) or m * u + m1 * 0 = (m + m1) * (2 * k *g * S)^(1/2) or u = [(m + m1) * (2 * k * g *S)^(1/2)/m] g = 9.8 m/s^2 substitute the values b)the final speed of the two sports car is zerotherefore v12 - v2 =2aS1 v1= 0 and S1 = 0.7 m or a = -(v2/2S1) = -((2* k * g * S)/2S1) or a = -(k * g * S/S1) the negative value of acceleration indicates that the motionof the two cars decreases with time.

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