We'll actually be covering more about this later, I think. In the
conveyer belt problem, we considered the velocity of the mass in the
frame of the factory (imagine you are on the floor and looking at the
crate and conveyer belt). In this frame the crate starts with zero
velocity when it's dropped onto the belt and ends up with some velocity with respect to you. In contrast, you
could consider the frame of the belt: imagine you are sitting
on the belt. In that frame, the crate would start with velocity 
(away from you) when it is dropped, and then reach the same velocity
as the belt-- so it would end up with zero velocity with respect to
you.
In the frame of the belt, as the crate comes to rest with respect to the belt, it's moving with respect to the belt (decelerated by friction). We calculated the distance it moved.
(If there were no friction, the crate would have zero
velocity with respect to the floor after dropping. The belt would
just slip under it. It would maintain velocity with respect to
the belt.)