The 1 kg box is sliding along a frictionless surface. it collides with and sticks to the 2 kg box. afterward, the speed of the two boxes is

  m/s  

If second object is at rest i.e. b = 0 m/s then final velocity after collision will be   m/s

Explanation: Let us consider the velocity of 1 Kg box = a m/s

and that of 2 Kg box = b m/s

So the linear momentum of 1 kg box will be = 1 a

Linear momentum of 2 Kg box = 2 b

Finally after collision both the masses stick together and move with a common velocity V m/s

So, applying the conservation of linear momentum

1 a + 2 b = (1 + 2) V

m/s  

If second object is at rest i.e. b = 0 m/s then final velocity after collision will be

m/s