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  • Please,please help me A particle of mass m is driven by a machine that delivers a constant power of k watts. If the particle starts from rest the force on the particle at time t is:

A particle of mass m is driven by a machine that delivers a constant power of  k watts. If the particle starts from rest the force on the particle at time t is:

  • Option 1)

      \sqrtt^{\frac{-1}{2}}

  • Option 2)

    \sqrt{2{mk}}t^{\frac{-1}{2}}

  • Option 3)

    \frac{1}{2}\sqrt mkt^{\frac{-1}{2}}

  • Option 4)

    \sqrt{\frac{mk}{2}}t^{\frac{-1}{2}}

 

Answers (1)

best_answer

As we learnt in

Power expressed as the rate of change of kinetic Energy -

P= frac{dk}{dt}

- wherein

dk ightarrow change: in: kinetic: energy

dt ightarrow interval: of : time:

 

 P=\frac{dw}{dt} = w= PT=\frac{1}{2}mv^2

v=\sqrt{\frac{2Pt}{m}}

acceleration =a=\frac{dv}{dt}=\sqrt{\frac{2P}{m}}.\frac{1}{2\sqrt{t}}

a=\frac{dv}{dt}=\sqrt{\frac{2P}{m}}.\frac{1}{2\sqrt{t}}

force =f=ma=\sqrt{\frac{2km^2}{m}}.\frac{1}{2\sqrt{t}}

=\sqrt{\frac{km}{2t}}=\sqrt{\frac{mk}{2}}t^\frac{-1}{2}


Option 1)

  \sqrtt^{\frac{-1}{2}}

Incorrect

Option 2)

\sqrt{2{mk}}t^{\frac{-1}{2}}

Incorrect

Option 3)

\frac{1}{2}\sqrt mkt^{\frac{-1}{2}}

Incorrect

Option 4)

\sqrt{\frac{mk}{2}}t^{\frac{-1}{2}}

Correct

Posted by

Aadil

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