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:
The total momentum must conserve before and after the collision.
1) Calling
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: