Problem 3.288

A wire bent as a parabola $y=a x^{2}$ is located in a uniform magnetic field of induction $B$, the vector $\mathbf{B}$ being perpendicular to the plane $x, y .$ At the moment $t=0$ a connector starts sliding translationwise from the parabola apex with a constant acceleration $w$ (Fig. 3.78). Find the emf of electromagnetic induction in the loop thus formed as a function of $y$.