There are several things going on here. The final answer is: no braking and no acceleration.
Assume a solenoid wound around a non-conducting rectangular form sloped at 45 degrees. A long magnetized rod magnetized end to end pulled or pushed through the solenoid will induce voltage pulses in the coil. If the ends of the solenoid are connected to a load, there will be a retarding force due to induced current. However, if a short rod magnetized end to end and rolling down the solenoid, will not induce a voltage, nor any retarding force. This is because both magnetized ends are at the same axial position of the solenoid at any instant in time.
Bob S