The velocity of the center of mass does not change by the collision. To see this, consider the center of mass at time t before collision and time t ′ after collision: x ¯ ¯ ( t ) = m A x A ( t ) + m B x B ( t ) m A + m B x ¯ ¯ ( t ′ ) = m A x A ( t ′ ) + m B x B ( t ′ ) m A + m B .