You are the juror of a case involving a drunken driver whose 1022 kg sports car

Question

You are the juror of a case involving a drunken driver whose 1022 kg sports car ran into a stationary 2043 kg station wagon stopped at a red traffic light. The cars stuck together and slid with locked wheels for 10.0 m before coming to rest. The coefficient of sliding friction on the dry road was 0.60. Estimate the speed of the sports car when it hit the station wagon. 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 0.9 m.

Explanation / Answer

By F(friction) = µ x mg

Ff = 0.6 x (1022 + 2043) x 9.8

Ff = 18022.2 N

W(friction) = Ff x s = 18022.2 x 10 = 180222 J

Let the velocity of the cars after the collision is v m/s,

By the work energy relation:-

W(friction) = KE

180222 = 1/2mv^2

180222 = 1/2 x (1022 + 2043) x v^2

v = 10.84 m/s

Let the initial speed of sports car was u m/s

By the law of momentum conservation:-

m1u1+m2u2 = (m1+m2)v

1022 x u + 0 = (1022 + 2043) x 10.84

u = 32.51 m/s

By v^2 = u^2 + 2as

(10.84)^2 = (32.51)^2 + 2 x a x 1

a = -469.7 m/s^2 [-ve is just indicating the direction i.e. it is retardation]

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