A car of mass 1000 kg travelling at a velocity of 25 m/s collides with another car of mass 1500kg which is at rest. The two cars stick and move off together. What is the velocity of the two cars after the collision?

The velocity of the two cars is 10 m/s after the collision.

Explanation:

Law Of Conservation Of Linear Momentum

The total momentum of a system of bodies is conserved unless an external force is applied to it. The formula for the momentum of a body with mass m and velocity v is

P=m.v

If we have a system of bodies, then the total momentum is the sum of them all

If some collision occurs, the velocities change to v' and the final momentum is:

In a system of two masses, the law of conservation of linear momentum  takes the form:

If both masses stick together after the collision at a common speed v', then:

The car of mass m1=1000 Kg travels at v1=25 m/s and collides with another car of m2=1500 Kg which is at rest (v2=0).

Knowing both cars stick and move together after the collision, their velocity is found solving for v':

v' = 10 m/s

The velocity of the two cars is 10 m/s after the collision.