Question

A particle is moving with velocity $\overrightarrow{V}=4x\hat{i}+4y\hat{j}$, then general equation for path of particle is

• A. $x=cy$
• B. $y=c{x}^2$
• C. $x^2-y^2=c^2$
• D. $x^2+y^2=c^2$

Answer 1

The correct option is A $x=cy$

Given, $\overrightarrow{V}=4x\hat{i}+4y\hat{j}$
differentiation w.r.t. $x$ and then $y$,
$V_x=\frac{dx}{dt}=4x$
$V_y=\frac{dy}{dt}=4y$
So, $\frac{dx}{dy}=\frac{x}{y}$ .....(1)

integrationg above equation,
$\int \frac{dx}{x}-\int \frac{dy}{y}=0lo{g}_{e}x-lo{g}_{e}y=c$
$\frac{x}{y}=c$
$x=cy$
Hence, option $A$ is correct answer.