Can motional emf be explained by faradays law?

Faraday’s law states that the potential difference between two points is equal to the rate of change flux through a loop containing both points. In the case of motional emf, there is no direct link to faradays law as the magnetic field is not varying but we can explain it through faradays law by doing some modifications. 

Consider two parallel rails and a rod of mass m and length l lying on both the rails perpendicular to both of them. Now we assume that the two parallel rails are connected by a wire through a resistance R so that they form a loop, now when the rod starts moving then the area of, this loop starts increasing and in an elemental time dt the area increased is v.dt so the change in flux = B.l.v.dt. The induced emf would be change of flux/time = Blv.dt/dt = bvl which is the same result that we calculate by balancing electric and magnetic force on an electron

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                -Arvin Gupta