A particle is moving with velocity v = K(y i + x j) , where K is a constant. The general equation for its path is: - Physics MCQ AIEEE 2026 | ExamTest.live

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

Solution & Step-by-step Explanation

Given v = Ky \hat{i} + K x \hat{j} .Comparing with v = v_{x} \hat{i} + v_{y} \hat{j} : v_{x} = \frac{d x}{d t} = Ky v_{y} = \frac{d y}{d t} = K x Dividing the two equations: \frac{d y / d t}{d x / d t} = \frac{K x}{Ky} \frac{d y}{d x} = \frac{x}{y} y d y = x d x Integrating both sides: \int y d y = \int x d x \frac{y ^{2}}{2} = \frac{x ^{2}}{2} + C^{'} y^{2} = x^{2} + constant

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

y = x^{2} + constant

y^{2} = x + constant

x y = constant

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

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