Finding the equation of motion in a magnetic field where a conductor rolls over two parallel infinite wires.

The conductor bridge is giving an initial velocity V0 to the right. The circuit completed by this bridge has an increasing area as the bridge moves to the right which means an increasing magnetic flux. Thus we know from Faraday's law that a current is created in the circuit completed by this bridge proportional to its velocity. So if the bridge continues to move freely forever, we have an infinite source of energy through generation of current. How is this violation of energy conservation resolved?

Find the equation of motion of the bridge and show that it slows down to rest eventually.