Consider two points in an electric field. The potential at point $1,$ V$1,$ is $31$ V$.$ The potential at point $2,$ V$2,$ is $187$ V$.$ An electron at rest at point $1$ is accelerated by the electric field to point $2.$

$$ Part $($a$)$

Write an equation for the change of electric potential energy $$U of the electron in terms of the symbols given.

$$ Part $($b$)$

Find the numerical value of the change of the electric potential energy in electron volts $($eV$).$

$$ Part $($c$)$

Express v$2,$ the speed of the electron at point $2,$ in terms of $$U$,$ and the mass of the electron me$.$

$$ Part $($d$)$

Find the numerical value of v$2$ in m$/$s$.$

v$2=$