A doubt regarding Lenz's Law

In one of the most common examples of Lenz's Law a magnet is dropped inside a copper tube and due the induced EMF and the eddy currents generated in the copper tube the magnet falls through it with constant velocity. The external force that the eddy currents oppose is obviously the acceleration due to gravity. So, the tube acts like a brake.

I have a simple doubt:

• If the magnet falls through with a constant initial velocity $v_0$ (with no external force i.e. no acceleration due to gravity present) would it still fall slowly due to eddy currents? And I assume the answer to it is again yes since any motion should generate an eddy current. But, how would the output velocity change when the magnet emerges from the other end of the tube?
• The thing you are suppose to have noted is that the velocity is 'initially constant' even though it is 'fall'ing. How could that be? How does that affect the answer to the question? Aug 26, 2017 at 17:29
• sorry what I meant is that there is no other external force, i.e. no acceleration due to gravity in my doubt. So input velocity is all we have. Aug 26, 2017 at 17:33