$\text{Force acting on particle of charge q }F = qE$

$ \text{Acceleration of the particle }a = \frac{qE}{m}$

$\text{Total distance covered d/2 , so time taken to strike the plate is t then}$

$ \frac{d}{2} = \frac{1}{2} at^2 = \frac{qEt^2}{2m}$

$ t = \sqrt {\frac{md}{qE}}$

$\text{Time taken to cross the length of plate is } t'= \frac{l}{v} =\frac{1}{2} \sqrt {\frac{md}{qE}}$

$\text{ Since t'< t so particle will cross the plate before striking any of plates}$