$4\mathrm{.}54$ An electron with charge $Q_e=-1\mathrm{.}6{10}^{-19}C$ and mass $m_e=9\mathrm{.}1{10}^{-31}kg$ is injected at a point adjacent to the negatively charged plate in the region between the plates of an air$-$filled parallel$-$plate capacitor with separation of $1$ cm and rectangular plates each $10c{m}^2$ in area $($Fig$.$ P$4\mathrm{.}54).$ If the voltage across the capacitor is $10$ V $,$ find the following:

$($a$)$ The force acting on the electron.

$($b$)$ The acceleration of the electron.

$($c$)$ The time it takes the electron to reach the positively charged plate, assuming that it starts from rest.

Figure P$4\mathrm{.}54$: Electron between charged plates of Problem $4\mathrm{.}54.$