A particle has $50\mathrm{.}6$ j of total potential energy and is moving at $2\mathrm{.}34$x$10\mathrm{⁴}$ m$/$s at some initial time. $21\mathrm{.}5$ J of work is done on the particle and at a later time has $134$ j of total potential energy. If the particles mass is $5\mathrm{.}35$x$10^-$⁷ what is its speed at a later time?