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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 $t = 2$.

A

$\cfrac{7}{3}$

B

$4$

C

$\cfrac{14}{3}$

D

$\cfrac{22}{3}$

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