If x = 2at, y = at2, then (d^2y)/(dx^2) is

Given,

$x=at^2$ and $y=2at$

On differentiating both sides w.r.t. t, we get,

$\frac{dx}{dt}=2a$ and $\frac{dy}{dt}=2at$

Therefore

$\frac{dy}{dx}=\frac{2at}{2a}=t$

Now, $\frac{d^2y}{dx^2}=\frac{d}{dt}(\frac{dy}{dx})×\frac{dt}{dx}⇒\frac{d}{dt}(t)×\frac{1}{2a}=1×\frac{1}{2a}=\frac{1}{2a}$

Option B is correct.