Let $x=2 t, y=\frac{t^2}{3}$ be a conic. Let $S$ be the focus and $B$ be the point on the axis of the conic such that $S A \perp B A$, where $A$ is any point on the conic. If $k$ is the ordinate of the centroid of $\Delta S A B$, then $\lim _{t \rightarrow 1}$ is equal to
