Speed of Car A Before Collision Analysis

Expert Witness Case Analysis:

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 7.20 m long, and inspection of the tire tread revealed that the coefficient of kinetic friction between the tires and the road was 0.650.

Question:

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

Final Answer:

To determine the speed of car A just before the collision, we can use the principles of conservation of momentum and work-energy theorem. By calculating the total momentum before the collision and equating it to the total momentum after the collision, we can find the initial velocity of car A. Using the work-energy theorem, we can also equate the work done by friction to the initial kinetic energy of car A.

Explanation:

To determine the speed of car A just before the collision, we can use the principles of conservation of momentum and work-energy theorem. Since the cars locked bumpers and slid to a stop, the total momentum before the collision is equal to the total momentum after the collision. We can also use the work-energy theorem to equate the work done by friction to the initial kinetic energy of car A.

Let V be the initial velocity of car A. The total momentum before the collision is the sum of the momentum of car A and car B, which can be expressed as V(1500 kg) + (0 kg)(0 m/s) = V(1500 kg).

From the work-energy theorem, the work done by friction is the force of friction multiplied by the distance of the skid marks. Therefore, the work done by friction is (0.650)(1500 kg)(9.8 m/s^2)(7.20 m) = 6876 J. This work done by friction is equal to the initial kinetic energy of car A, which is (1/2)(1500 kg)(V^2).

Setting these two expressions for work equal to each other and solving for V, we find V = 7.93 m/s. Therefore, the speed of car A just before the collision was 7.93 m/s.