Q 11-03-157JEE MainJEE Main 2019 (9 Jan, Shift 1)Easy
A particle is moving with a velocity $\vec v = K(y\hat i + x\hat j)$, where $K$ is a constant. The general equation for its path is
Answer: (D) $y^2 = x^2 + \text{constant}$
The slope of the path is the ratio of the velocity components:
$$\frac{dy}{dx} = \frac{v_y}{v_x} = \frac{Kx}{Ky} = \frac{x}{y}$$
Separating variables, $y\,dy = x\,dx$, and integrating:
$$y^2 = x^2 + \text{constant}$$
Solution by Sreeraj P, M.Sc Physics