Answer
$v$ = 69.14 x $10^6$ m/s = 69.14 Mm/s
Work Step by Step
Initial Voltage $V_{i}$ = 17 kJ/C
Final Voltage $V_{f}$ = 6 kJ/C
Charge $q$ = -1.6 x $10^{-19}$ C
Mass $m$ = 9.1 x $10^{-31}$kg
Initial potential energy $U_i$ = $q$ x $V_i$
Final potential energy $U_i$ = $q$ x $V_f$
Initial velocity $u$ = 93 x $10^6$ m/s
Final velocity $v$ = ?
Since only conservative electrostatic force acts on the charge energy is conserved.
($U_f$ - $U_i$) + ($K_f$ - $K_i$) = 0
[- 1.6 x $10^{-19}$ x (6 - 17) x $10^3$ ] + [0.5 x 9.1 x $10^{-31}$ x ($v^2$ - $u^2$)] = 0
$v^2$ = 47.81 x $10^{14}$
$v$ = 69.14 x $10^6$ m/s = 69.14 Mm/s
