Well, if you're talking about an electric motor, then it should go roughly as follows. An electric motor works by spinning a pair of electromagnets inside of a permanent magnet (see
Howstuffworks for a more detailed description). The electromagnets in this setup will have a magnetic field which depends on the properties of the solenoid:
[tex]B=\mu in[/tex]
where B is the magnetic field, [tex]\mu[/tex] is the permeability of the object around which the wires are wrapped, i is the current through the solenoid, and n is the number of turns per unit length. This magnetic field will vary linearly with the current, so cutting the current by a third should cut the magnetic field by a third.
As for the velocity, I would imagine you can approximate the two solenoids as a magnetic dipole in an external field created by the permanent magnet. The potential energy of such a setup would be given by
[tex]U=-\mu_{magnet} \bullet B_{ext}[/tex]
where this time mu is the magnetic dipole moment of the electromagnet. The maximum kinetic energy that can be extracted from such a setup is just equal to the maximum magnitude of the potential, so you'd expect
[tex]v_{max} \propto \sqrt{U} \propto \sqrt{\mu_{magnet}} \propto \sqrt{i}[/tex]
This is only a very rough argument, however, and I doubt that things are so nicely linear in practice.
