A particle moves in a circular path such that its speed v varies with distance as V=αs where α is a positive constant. Find the acceleration of the particle after traversing a distance s.

at=VdVds=αsd(αs)ds=αs⋅α2s=α2/2ac=V2R=α2sRNet acceleration, anet=at2+ac2=α214+s2R2

A particle moves in a circular path such that its speed v varies with distance as V=αs where α is a positive constant. Find the acceleration of the particle after traversing a distance s.

at=VdVds=αsd(αs)ds=αs⋅α2s=α2/2ac=V2R=α2sRNet acceleration, anet=at2+ac2=α214+s2R2

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A particle moves in a circular path such that its speed v varies with distance as $V = α \sqrt{s}$ where $α$ is a positive constant. Find the acceleration of the particle after traversing a distance s.

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$α^{2} \sqrt{\frac{1}{4} + \frac{s^{2}}{R^{2}}}$

$α^{2} \sqrt{\frac{R^{2}}{4 s^{2}} + \frac{s^{2}}{R^{2}}}$

$α \sqrt{\frac{1}{4} + \frac{s^{2}}{R^{2}}}$

$α \sqrt{\frac{R^{2}}{4 s^{2}} + \frac{s^{2}}{R^{2}}}$

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$a_{t} = V \frac{d V}{d s} = α \sqrt{s} \frac{d (α \sqrt{s})}{d s} = α \sqrt{s} \cdot \frac{α}{2 \sqrt{s}} = α^{2} / 2$

$a_{c} = \frac{V^{2}}{R} = \frac{α^{2} s}{R}$

Net acceleration, $a_{n e t} = \sqrt{{a_{t}}^{2} + {a_{c}}^{2}} = α^{2} \sqrt{\frac{1}{4} + \frac{s^{2}}{R^{2}}}$

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A particle moves in a circular path such that its speed v varies with distance as V=αs where α is a positive constant. Find the acceleration of the particle after traversing a distance s.

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A particle moves in a circular path such that its speed v varies with distance as $V = α \sqrt{s}$ where $α$ is a positive constant. Find the acceleration of the particle after traversing a distance s.