Dear Student,
After sometime, the magnet will move with a constant velocity inside the tube.
Here ,the magnet is released from rest in the copper tube.No other forces are acting on it initially.Hence it moves with a constant acceleration g.Due to this non zero acceleration,the flux linked with the copper tube will be changing continously.According to Lenz's Law, to opposes the change in flux, a current and magnetic field will be induced in the copper tube. This induced field will repel the the magnet in the direction opposite to its motion.Hence, initially it will have a lower speed. Eventually the magnetic repulsion due to induced field by Lenz's Law will become equal to the gravitational force on the magnet.After this, the net force on the magnet becomes zero.Therefore, its falling freely and will reach a constant velocity.
Regards.