A particle of mass $5\,\text{kg}$ moving in the $X$-$Y$ plane has its potential energy given by $U = (-7x + 24y)\,\text{J}$. The particle is initially at the origin and has a velocity $\vec{v} = (14.4\,\hat{i} + 4.2\,\hat{j})\,\text{m/s}$.