At time $t\geq 0$, a particle moving along a curve in the xy-plane has position $\left ( x(t),y(t) \right )$ with velocity vector $v(t)=\left ( t^{2},e^{0.4t} \right )$.

At $t = 1$, the position of the particle is at the point $(5,4)$.

Find the $x$-coordinate of the position of the particle at time $t = 2$.