Electromagnetic Induction - rod on two parallel tracks, force varies

[dharavsolanki]

Homework Statement

Two infinite parallel wires, having the cross sectional area 'a' and resistivity 'k' are connected at a junction point 'P'. A slide wire of negligible resistance and having mass 'm5 and length l can slide between the parallel wires, without any frictional resistance.

If the system of wires is introduced to ' a magnetic field of intensity "B" (into the plane of paper) and the slide wire is pulled with a force which varies with the velocity of the slide wire
as F = F0V, then find the velocity of the slide wire as a function of the distance travelled. (The slide wire is initially at origin and has a velocity v0)

Homework Equations

Relation between flux and induced electric field.
Force on a current carrying conductor in a magnetic field.
Relation between resistance and resistivity, length and cross sectional area.
Calculus?

The Attempt at a Solution

When the rod is moved, flux changes and the electric current is induced, which introduces another force. But the force on this is variable. How do I solve the question in such a situation?

 

[member 553083]

I think we need to calculate the force, and then use the equation F=ma to get the acceleration. Then integrate this to get the velocity as a function of distance. But I'm not sure how to calculate the force.