A particle with charge $3\mathrm{.}201019$ CC is placed on the x axis in a region where the electric potential due to other charges increases in the $+$x direction but does not change in the y or z direction. The particle, initially at rest, is acted upon only by the electric force and moves from point a to point b along the x axis, increasing its kinetic energy by $1\mathrm{.}121018$ JJ $.$ In what direction and through what potential difference Vb$$VaVb$$Va does the particle move?

View Available Hint$($s$)$for Part A

The particle moves to the left through a potential difference of Vb$$Va$=$Vb$$Va$=3\mathrm{.}50$ VV $.$The particle moves to the left through a potential difference of Vb$$Va$=$Vb$$Va$=-3\mathrm{.}50$ VVThe particle moves to the right through a potential difference of Vb$$Va$=$Vb$$Va$=3\mathrm{.}50$ VV $.$The particle moves to the right through a potential difference of Vb$$Va$=$Vb$$Va$=-3\mathrm{.}50$ VV $.$The particle moves to the left through a potential difference of Vb$$Va$=$Vb$$Va$=35\mathrm{.}0$ VV $.$The particle moves to the right through a potential difference of Vb$$Va$=$Vb$$Va$=-35\mathrm{.}0$ VV $.$ If the particle moves from point b to point c in the y direction, what is the change in its potential energy, Uc$$UbUc$$Ub$?$

View Available Hint$($s$)$for Part B

$++1\mathrm{.}121018$ JJ$1\mathrm{.}121018$ JJ$0$