A 13,500 kg railroad freight car travels on a level track at a speed of 4.5 m/s. It collides and couples with a 25,000 kg second car, initially at rest. What is the speed of the two cars after the collision?

Given: The mass of the first car is 13,500 kg. 

           The speed of the first car is 4.5 m/s. 

           The mass of the second car is 25,000 kg. 

To determine: The speed of the two cars after the collision. 

Assume the direction of the first car as positive, 

The momentum of the system is conserved,

$m_1{v}_1+m_2{v}_2=m_{1}v{\text{'}}_1+m_{2}v{\text{'}}_2$ ............................ (1)

where $m_1$ is the mass of the first car, $m_2$ is the mass of the second car, $v_1$ is the velocity of the first car before the collision, $v_2$ is the velocity of the second car after the collision, $v_1\text{'}$ is the velocity of the first car after the collision and $v_2\text{'}$ is the velocity of the second car after the collision.