Physics Question from JEE Main 2024 · 27 January, Shift 1

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