To a close approximation, the pressure behind a rifle bullet varies inversely with the position $x$ of the bullet along the barrel. Thus the acceleration of the bullet $m$ constant. If the bullet starts from rest at $a=5\mathrm{.}9mm$ and if the muzzle velocity of the bullet is $592\frac{m}{s}$ at the end of the $753\mathrm{.}3mm$ barrel, compute the acceleration midpoint of the barrel at $x=\frac{753\mathrm{.}3}{2}mm.$