A bar magnet is overhanging north end up well above a vertical coil of wire. The bar magnet is released and as it falls down toward the coil it falls along a path that will take it straight through the coil. While it is decreasing downward toward the coil is a current induced to flow in the coil as a result of the motion of the magnet?

Answer:

As time departs by while the magnet is falling toward the coil the coil becomes closer and closer to the magnet not because of the motion of the coil but rather in this case for the reason that of the motion of the magnet.

The nearer the coil is to the magnet the stronger the magnetic field at the location of the coil due to the magnet and with the given orientations and relative position of magnet and coil that means in this case the greater the number of magnetic field lines through the coil.

By Faraday's Law of induction a changing numerous field lines through a closed loop or coil induces a current to flow in that loop or coil. For the reason that the coil becomes closer and closer to the magnet the number of magnetic field lines through the coil is increasing with time and as a result of this changing magnetic-field-through-the-coil there is indeed a current induced to flow in the coil.