a) Let x be the distance from the right end of the rails to the rod and find an expression for the magnetic flux through the area enclosed by the rod and rails. Set up the integral for the magnetic flux spanning the area of the loop with rectangular strips with dA = x dr located a distance r from the long straing wire. After finding the flux, determine the induced emf by differentiating with respect to t (only x depends on t!).
b - e) Remainder of solution follows my presentation in class on the subject of motional emf. In part d) however the magnetic field along the rod is not constant so you will need to integrate dF along the rod.