A 1250 kg car is moving down the highway with a velocity of 32.0 m/s when it bumps into the car ahead of it which has a mass of 875 kg and a velocity of 25.0 m/s. After the collision, the two cars stick together. What will be the resulting velocity of the two cars together? How much energy will be lost in this collision?

Question

anonymous · Answer

For this you can use conservation of momentum to find the final velocity, and then calculate the kinetic energy of the system both before and after the collision. Since we know that the cars stick together, the final velocity for both will be the same, and so can be expressed as their combined masses times the final velocity of the hunk of cars. 

$$p_i=p_f$$
$$m_1v_{1i}+m_2v_{2i}=(m_1+m_2)v_{f}$$

Solve for Vf

Then to find how much energy was lost, use the formula for kinetic energy of an object

$$K=\frac{1}{2}mv^2$$
to find the total energy of both cars before the collision, then compare it to the kinetic energy of the car-hunk-mess after the collision.