A particle starts from origin at t =0 with a velocity 5 i m / s and moves in x-y plane under action of a force which produces a constant acceleration…

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