A particle starts from origin at $t = 0$ with a velocity $5{\rm{\hat im}}/{\rm{s}}$ and moves in $x - y$ plane under action of a force which produces a constant acceleration of $(3\hat \imath + 2\hat \jmath ){\rm{m}}/{{\rm{s}}^2}$. If the $x$-coordinate of the particle at that instant is 84 m , then the speed of the particle at this time is $\sqrt \alpha {\rm{m}}/{\rm{s}}$. The value of $\alpha $ is