Power supplied to a particle of mass 2, kg varies with time as P = frac{{3{t^2}}}{2} watt . Here, t

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5.Work, Energy, Power and Collision

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Power supplied to a particle of mass $2\, kg$ varies with time as $P = \frac{{3{t^2}}}{2}$ $watt$ . Here, $t$ is in $seconds$ . If velocity of particle at $t = 0$ is $v = 0$, the velocity of particle at time $t = 2\, s$ will be ............ $\mathrm{m}/ \mathrm{s}$

A

$1$

B

$4$

C

$2$

D

$2\sqrt 2$

Solution

$P=\frac{3 t^{2}}{2}$

$\mathrm{mv} \frac{\mathrm{dv}}{\mathrm{dt}}=\frac{3 \mathrm{t}^{2}}{2}$

$\frac{V^{2}}{2}=\frac{3 t^{3}}{3 \times 4}$

$\frac{V^{2}}{2}=\frac{t^{3}}{4}$

at $t=2$

$\mathrm{V}=2 \mathrm{m} / \mathrm{s}$

Standard 11

Physics

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