A particle is moving with a velocity vecv = K (y hati + x hatj) , where K is a constant. The general equation for its path is:

Question

A particle is moving with a velocity vecv = K (y hati + x hatj) , where K is a constant. The general equation for its path is: (A) xy = constant (B) y2 = x2 + constant (C) y = x2 + constant (D) y2 = x + constant

Tardigrade Admin · Accepted Answer

(dx/dt) = ky, (dy/dt) =kx Now, (dy/dx) = ((dy/dt)/(dx)dt) = (x/y) ⇒ ydy = xdx Integrating both side y2 = x2 +c

Q. A particle is moving with a velocity $v = K (y \hat{i} + x \hat{j})$ , where $K$ is a constant. The general equation for its path is:

$x y$ = constant

$y^{2} = x^{2} +$ constant

$y = x^{2} +$ constant

$y^{2} = x +$ constant

$\frac{d x}{d t} = k y, \frac{d y}{d t} = k x$
Now, $\frac{d y}{d x} = \frac{\frac{d y}{d t}}{\frac{d x}{d t}} = \frac{x}{y}$
$\Rightarrow y d y = x d x$
Integrating both side
$y^{2} = x^{2} + c$

Q. A particle is moving with a velocity v=K(yi^+xj^​) , where K is a constant. The general equation for its path is:

xy = constant

y2=x2+ constant

y=x2+ constant

y2=x+ constant