A parallel plates capacitor is made of square conducting plates of side a and the separation between plates is d. The capacitor is connected with battery of emf V volt as shown in the figure. There is a dielectric slab of dimension $a\times a\times d$  with dielectric constant k. at $t = 0$, dielectric slab is given velocity $v_0$ towards capacitor as shown in the figure. (Neglect the effect of gravity and electrostatic force acting on the dielectric when dielectric is outside the capacitor. Also ignore any type of frictional force acting on the dielectric during its motion) Let the x be the length of dielectric inside the capacitor at $t=t sec$, (Mass of the dielectric is m and Capacitor plates are fixed,  ${\mathcal{l}}_0\gg a$)