An electron is placed $($starting at rest$)$ at the vertical negative plate across an electric field from a vertical positive plate. When released, the electron moves horizontally across the field and strikes the positive plate with a velocity of $4\mathrm{.}00$ x ${10}^6\frac{m}{s}.$

a$)$ Determine the potential difference between the two plates.$(3$ marks$)$

b$)$ If the distance between the two plates is $3\mathrm{.}00$ cm $,$ find the electric field strength.$(3$ marks$)$

c$)$ Determine the acceleration of the electron within the electric field.$(3$ marks$)$