A particle located at x = 0 at time t = 0 , starts moving along the positive x -direction with a velocity v that varies as v = α √(x) . The displaceme - Physics MCQ AIEEE 2006 2026 | ExamTest.live

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A particle located at x = 0 at time t = 0, starts moving along the positive x -direction with a velocity v that varies as v = α x . The displacement of the particle varies with time as:

Solution & Step-by-step Explanation

Given velocity v = α x .Since v = \frac{d x}{d t}, we have: \frac{d x}{d t} = α x Separating variables and integrating: \int_{0}^{x} \frac{d x}{x} = \int_{0}^{t} α d t [2 x]_{0}^{x} = [α t]_{0}^{t} 2 x = α t Squaring both sides: 4 x = α^{2} t^{2} ⟹ x = \frac{α ^{2}}{4} t^{2} Therefore, x \propto t^{2} .

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A particle located at x = 0 at time t = 0, starts moving along the positive x -direction with a velocity v that varies as v = α x . The displacement of the particle varies with time as:

t^{3}

t^{2}

t

t^{1/2}

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