A2.0 kilogram cart moving due east at 6.0 meters per second collides with a 3.0 kilogram cart moving due west. the carts stick together and come to rest after the collision. what was the initial speed of the 3.0 kilogram cart?

Hello

The total momentum must conserve before and after the collision.

1) Calling  and  the masses of the two carts, and and the velocities of the two carts before the collision, the initial momentum is

where the negative sign means the two carts are moving into opposite directions.

2) The two carts after collision are at rest, this means the total momentum after collision is 


3) Since the momentum must be conserved, we can write 

and  substituting

from which we can get the velocity of the second cart: