Power supplied to a particle of mass 2kg

Asked by admin @ 24/08/2021 in Physics viewed by 307 People

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

a)1m/s b)4m/s c) 2m/s d)2*21/2m/s

Answered by admin @ 24/08/2021

Answer:

So,option (c) is correct.

Explanation:

Since we know that the power is defined as the multiple of force and velocity.

$P =Fv$ ..................(1)

We know the expression for force from newton second law of motion,

$F=m\dfrac{dv}{dt}$ ............(2)

From (1) and (2) we get,

$P =m\frac{dv}{dt}v\\\\Pdt=mvdv$

Integrate both sides,

$\int\ {\dfrac{3t^{2}}{2}} \, dt=\int\ {mv} \, dv\\ \\\dfrac{t^{3} }{2}=m\dfrac{v^{2}}{2}$

So, velocity of particle at t =2 seconds is

$\dfrac{8}{2}=\dfrac{2v^{2}}{2}$

$v =2 m/s$

So,option (c) is correct.

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