A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P_{o}. The instantaneous velocity of this car is proportional to

  • Option 1)

    t^{2} P_{o}

  • Option 2)

    t^{1/2}

  • Option 3)

    t ^{-1/2}

  • Option 4)

    \frac{1}{\sqrt{m}}

 

Answers (1)
V Vakul

As discussed in

Power if the force is variable -

P_{av}= frac{Delta w}{Delta t}= frac{int_{0}^{t}pcdot dt}{int_{0}^{t}dt}

- wherein

P
ightarrow power

dt
ightarrow short: interval : of: time

 

 P_{0} = FV = m \frac{dv}{dt} v

P_{0} dt = m v dv \Rightarrow P_{0}\int dt = m \int vdv

P_{0}t = \frac{mv^{2}}{2} = v = \sqrt{\frac{2P_{0}t}{m}}

v\propto \sqrt{t} \Rightarrow v\propto t^{\frac{1}{2}}


Option 1)

t^{2} P_{o}

This solution is incorrect

Option 2)

t^{1/2}

This solution is correct

Option 3)

t ^{-1/2}

This solution is incorrect

Option 4)

\frac{1}{\sqrt{m}}

This solution is incorrect

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