Initially a particle of mass $6$ is travelling at velocity $v=\frac{1}{\sqrt[\phantom{2}]{3}}$ in one dimension, and is at position $x=-5.$ The only force it feels is an air resistance such that $F=-4v^3-4v.$ First, find the velocity of the particle as a function of $x.$

$v(x)=$

Now determine the distance $L$ that the particle travels before coming to rest.

$L=$