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 a car of mass 1900 kg (car A) which approached a stationary car of mass 1000 kg (car B). The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 15 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.6. Prove to the court that the driver of car A was exceeding the 55-mph speed limit before applying his brakes.

Explanation / Answer

The mass of car A is m1 = 1900 kg The mass of car B is m2 = 1000 kg The driver of car A applied his brakes S = 15 m before he crashed into car B. After the collision, car A slid S1= 15 m while car B slid S2 = 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be µk = 0.6. According to the law of conservation of momentum,we have m1u1 + m2u2 = m1v1 + m2v2 or u1 = (m1v1 + m2v2 - m2u2/m1) where v1 = (µkgS1)^1/2,v2 = (µkgS2)^1/2,u2 = 0 and g = 9.8 m/s2 The speed limit before applying the brakes is V = 55-mph = 55 * (1/3600) m/s = 0.0152 m/s The speed limit before applying the brakes is V = 55-mph = 55 * (1/3600) m/s = 0.0152 m/s

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