A ball of mass 4 kg , moving with a velocity of 10 $\mathrm{ms}^{-1}$, collides with a spring of length 8 m and force constant $100 \mathrm{Nm}^{-1}$. The length of the compressed spring is $x \mathrm{~m}$. The value of $x$, to the nearest integer, is $\_\_\_\_$ .
