$(35$ pts$.)$ A spring with an unstretched length of $0\mathrm{.}2$ m and a k $($spring constant$)$ value of $12000\frac{N}{m}$ is used to push a $5-$kilogram box from a length of $0\mathrm{.}1$ m to a length of $0\mathrm{.}2$ m horizontally. If the box starts at rest, what would you expect the final velocity to be$?g=0\mathrm{.}81\frac{m}{s^2}.$ Neglect the frictional forces. $($Hints: Conservation of Energy$)$