Physics Homework Help?

Question

A 950-kg sports car collides into the rear end of a 2100-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.5 m before stopping. The police officer, estimating the coefficient of kinetic friction between tires and road to be 0.80, calculates the speed of the sports car at impact.

 

What was the speed sports car at impact?

Answer 1

Step 1:

The mass of the sports car is 950 kg.

Let speed of sports car before impact be .

Let speed of both vehicles after impact be  .

The mass of the SUV is 2100 kg.

Coefficient of kinetic friction between tires and road is 0.8.

Momentum before collision is .

Momentum after collision is .

Law of conservation of momentum:

Step 2:

Frictional force is .

Work done by fictional force is .

Total kinetic energy of both cars after impact .

From (2) and (3),

Substitute in expression (1).

Speed of the sports car at the impact is .

Solution:

Speed of the sports car at the impact is .