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  • Solve! A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude Po. The instantaneous velocity of this car is proportional to:

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

  • Option 1)

    \text{t}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}

  • Option 2)

    \text{t}^{{{ - 1} \mathord{\left/ {\vphantom {{ - 1} 2}} \right. \kern-\nulldelimiterspace} 2}}

  • Option 3)

    {\text{t} \mathord{\left/ {\vphantom {\text{t} {\sqrt \text{m} }}} \right. \kern-\nulldelimiterspace} {\sqrt \text{m} }}

  • Option 4)

    \text{t}^\text{2} \text{P}_\text{o}

 

Answers (1)

best_answer

As we learned in

\int Vdv\:=\:\int \frac{Pdt}{m}        

After integrating

V\:=\:(\frac{2Pt}{m})^{\frac{1}{2}}

V\:\propto \:t^{\frac{1}{2}}

 


Option 1)

\text{t}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}

This option is correct.

Option 2)

\text{t}^{{{ - 1} \mathord{\left/ {\vphantom {{ - 1} 2}} \right. \kern-\nulldelimiterspace} 2}}

This option is incorrect.

Option 3)

{\text{t} \mathord{\left/ {\vphantom {\text{t} {\sqrt \text{m} }}} \right. \kern-\nulldelimiterspace} {\sqrt \text{m} }}

This option is incorrect.

Option 4)

\text{t}^\text{2} \text{P}_\text{o}

This option is incorrect.

Posted by

prateek

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