Power supplied to a particle of mass 2kg varies with time as P=3t22W . 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

From work energy theoremΔ KE=Wnetor Kf-Ki=∫Pdt or 12mv2=∫02(32t2) dt or v2=[t32]02 or v=2 m/s

Power supplied to a particle of mass 2kg varies with time as P=3t22W . 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

From work energy theoremΔ KE=Wnetor Kf-Ki=∫Pdt or 12mv2=∫02(32t2) dt or v2=[t32]02 or v=2 m/s

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

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$1 m / s$

$4 m / s$

$2 m / s$

$2 \sqrt{2} m / s$

answer is C.

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Detailed Solution

From work energy theorem
$Δ K E = W_{n e t}$
or $K_{f} - K_{i} = \int Pd t$
or $\frac{1}{2} m v^{2} = \int_{0}^{2} (\frac{3}{2} t^{2}) d t$
or $v^{2} = {[\frac{t^{3}}{2}]}_{0}^{2}$
or $v = 2 m / s$

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Power supplied to a particle of mass 2kg varies with time as P=3t22W . 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 $2 kg$ varies with time as $P = \frac{3 t^{2}}{2} W$ . Here t is in second. If velocity of particle at $t = 0$ is $v = 0$ . The velocity of particle at time $t = 2 s$ will be