A particle is moving with speed v - bsqrt-x- along positive x-axis- Calculate the speed of the particle time t - tau -assume that the particle is origin t - 0-dfrac-b-2 tau-4-dfrac-b-2 tau-2-b-2 taudfrac-b-2 tau-sqrt-2-

The correct option is B b2-x3C4-2v-b-x221A-xdvdt-b2-x221A-xdxdt

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Question

A particle is moving with speed $v = b \sqrt{x}$ along positive x-axis. Calculate the speed of the particle at time $t = τ$ (assume that the particle is at origin at $t = 0$ )
$\frac{b^{2} τ}{4}$
$\frac{b^{2} τ}{2}$
$b^{2} τ$
$\frac{b^{2} τ}{\sqrt{2}}$

b^{2} τ

\frac{b^{2} τ}{4}

\frac{b^{2} τ}{\sqrt{2}}

\frac{b^{2} τ}{2}

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Solution

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The correct option is B $\frac{b^{2} τ}{2}$
$v = b \sqrt{x}$
$\frac{d v}{d t} = \frac{b}{2 \sqrt{x}} \frac{d x}{d t}$

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The correct option is B b2τ2v=b√xdvdt=b2√xdxdt

A particle is moving with speed $v = b \sqrt{x}$ along positive x-axis. Calculate the speed of the particle at time $t = τ$ (assume that the particle is at origin at $t = 0$ )
$\frac{b^{2} τ}{4}$
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The correct option is B $\frac{b^{2} τ}{2}$
$v = b \sqrt{x}$
$\frac{d v}{d t} = \frac{b}{2 \sqrt{x}} \frac{d x}{d t}$