Power supplied to a particle of mass 2kg varies with time as P=3t22watt. Here t is in second. If velocity of particle at t= 0 is v = 0. The velocity of particle at time t = 2s will be

P=3t22⇒FV=3t22⇒mav=3t22⇒m.dvdtv=3t22⇒mdvdt×v=3t22⇒m dv×v=3t22dt⇒m ∫ v dv=32∫02t2dt⇒2×v22=32×t3302⇒v2=4v=2m/s

Power supplied to a particle of mass 2kg varies with time as P=3t22watt. Here t is in second. If velocity of particle at t= 0 is v = 0. The velocity of particle at time t = 2s will be

P=3t22⇒FV=3t22⇒mav=3t22⇒m.dvdtv=3t22⇒mdvdt×v=3t22⇒m dv×v=3t22dt⇒m ∫ v dv=32∫02t2dt⇒2×v22=32×t3302⇒v2=4v=2m/s

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

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$2 \sqrt{2} m / s$

$1 m / s$

$2 m / s$

$4 m / s$

answer is C.

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Detailed Solution

$P = \frac{3 t^{2}}{2} \Rightarrow F V = \frac{3 t^{2}}{2}$

$\Rightarrow m a v = \frac{3 t^{2}}{2} \Rightarrow m . \frac{d v}{d t} v = \frac{3 t^{2}}{2}$

$\Rightarrow m \frac{d v}{d t} \times v = \frac{3 t^{2}}{2}$

$\Rightarrow m d v \times v = \frac{3 t^{2}}{2} d t$

$\Rightarrow m \int v d v = (\frac{3}{2}) \int_{0}^{2} t^{2} d t$

$\Rightarrow 2 \times \frac{v^{2}}{2} = \frac{3}{2} \times {(\frac{t^{3}}{3})}_{0}^{2}$

$\Rightarrow v^{2} = 4$

$v = 2 m / s$

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Power supplied to a particle of mass 2kg varies with time as P=3t22watt. Here t is in second. If velocity of particle at t= 0 is v = 0. The velocity of particle at time t = 2s will be

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