Parametric, Polar and Vector-Valued Functions · Hard problem

A particle has position $\mathbf{r}(t)=\langle t^2,\;t^3\rangle$. Find the tangential component of its acceleration, $a_T=\dfrac{\mathbf{v}\cdot\mathbf{a}}{|\mathbf{v}|}$, at $t=1$.