If $x=a t^2, y=2 a t$, then $\frac{d^2 y}{d x^2}$ is equal to:

$-\frac{1}{2 a t^2}$ $-\frac{1}{2 a t^3}$ $\frac{1}{t^3}$ $\frac{1}{t^2}$

$-\frac{1}{2 a t^3}$

The correct answer is Option (2) → $-\frac{1}{2 a t^3}$