Difficult# Finding Position Vector from Acceleration Functions

APCALC-S51JAL

A particle travels along a path described parametrically by:

${ a }_{ x }={ t }^{ 2 }$

${ a }_{ y }=\cos(2t+3)$

If the particle starts from rest and has a final $x=833.333$, what is the position of the particle at $t=10\text{s}$ in vector notation?