## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

(a) $U_{1 \to 2}=U_{1 \to 3}$ (b) $v_{2}=v_{3}$
(a) Potential energy of the charge in an electric field is $U=qEs$. Here, $s$ is the distance measured vertically from point $1$ to point $2$ as there is no horizontal component of $E$. Hence, $U_{1 \to 2}=U_{1 \to 3}$. (b) Since, total energy is constant , hence the change in the kinetic energy $\Delta K_{12}$ is equal to $\Delta K_{13}$ because $\Delta U_{12}=\Delta U_{13}$. Hence, $v_{2}=v_{3}$.