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A body of mass m  accelerates uniformly from rest   to \nu  in time T  The instantaneous power delivered to the body as a function of time is given by 

Option 1)

\frac{1}{2}\frac{m\nu ^{2}}{T^{2}}t

 Option 2)

\frac{1}{2}\frac{m\nu ^{2}}{T^{2}}t^{2}
Option 3)

\frac{m\nu ^{2}}{T^{2}}\cdot t

 Option 4)

\frac{m\nu ^{2}}{T^{2}}\cdot t^{2}

Answers (2)

best_answer

As we learnt in

Power if the force is constant -

P=\frac{dw}{dt}= P= \vec{F}\cdot \vec{v}

- wherein

\vec{F}\rightarrow force

\vec{v}\rightarrow velocity

 

 Acceleration =\frac{v}{T}

at any time t, velocity v =(\frac{v}{T})t               ........(1)

Instantaneous power P = Fv

P=(ma).v

    =m(\frac{v}{T}).(\frac{v}{T})t

P=m\frac{v^{2}}{T^{2}}t

Correct answer is 3


Option 1)

\frac{1}{2}\frac{m\nu ^{2}}{T^{2}}t

This is an incorrect option.

Option 2)

\frac{1}{2}\frac{m\nu ^{2}}{T^{2}}t^{2}

This is an incorrect option.

Option 3)

\frac{m\nu ^{2}}{T^{2}}\cdot t

This is the correct option.

Option 4)

\frac{m\nu ^{2}}{T^{2}}\cdot t^{2}

This is an incorrect option.

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