A constant electric field accelerates a proton from rest through a distance of $1\mathrm{.}55m$ to a speed of $1\mathrm{.}65{10}^5\frac{m}{s}.($The mass and charge of a proton are $m_p=1\mathrm{.}67{10}^{-27}kg$ and $q_p=e=1\mathrm{.}60{10}^{-19}C.)$

$($a$)$ Find the change in the proton's kinetic energy $($in J$).$

$($b$)$ Find the change in the system's electric potential energy $($in J$).$

$($c$)$ Calculate the magnitude of the electric field $($in N$/$C$).$

N$/$C