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  • Need explanation for: - Work Energy and Power - JEE Main

A body of mass m  accelerates uniformly from rest   to \nu _{1}  in time t_{1}  The instantaneous power delivered to the body as a function of time t is

Option 1)

\frac{m\nu _{1}t}{t_{1}}

 Option 2)

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

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

 Option 4)

\frac{m\nu{_{1}}^{2}t}{t_{1}}

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

 

 Initial velocity = 0 

Final velocity = v1

Time taken = t1

Acceleration =\frac{v_{1}}{t_{1}}

\therefore    velocity at time t=(\frac{v_{1}}{t_{1}})t

Power delivered at time t

    = F. v

    = ma .v 

P=m(\frac{v_{1}}{t_{1}}).(\frac{v_{1}}{t_{1}})t

P=m\frac{v_{1}^{2}}{t_{1}^{2}} t

Correct answer is 2

 


Option 1)

\frac{m\nu _{1}t}{t_{1}}

This is an incorrect option.

Option 2)

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

This is the correct option.

Option 3)

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

This is an incorrect option.

Option 4)

\frac{m\nu{_{1}}^{2}t}{t_{1}}

This is an incorrect option.

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