If you move the magnet twice as fast in and out of the coil of wire, the rate at which the magnetic field through the coil changes will also double. According to Faraday's law of electromagnetic induction, the induced electromotive force (emf) in a coil is directly proportional to the rate of change of the magnetic field through the coil. Therefore, if the magnet is moved twice as fast, the induced emf and thus the current in the coil will also double.
