If $x=at^2$ and $y=2at$, then $\frac{d^2

CUET Preparation Today

Start Free Mocks

Home Questions CAAGNTKUB6

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Continuity and Differentiability

Question:

If $x=at^2$ and $y=2at$, then $\frac{d^2 y}{d x^2}$ is

Options:

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

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

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

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

Correct Answer:

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

Explanation:

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

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

$\frac{dy}{dx}=\frac{1}{t}$ so $\frac{d^2t}{dx^2}=\frac{-1}{t^2}\frac{dt}{dx}$

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