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 from Physics Work, Energy and Power Class 11 Manipur Board
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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

  • t2Po

  • t1/2

  • t-1/2

  • bevelled fraction numerator straight t over denominator square root of straight m end fraction

B.

t1/2

Power Po = Fv
equals open parentheses straight m dv over dt close parentheses straight v
equals space mv dv over dt
Integrating space both space sides
integral straight P subscript straight o dt space equals integral mv space dv
straight P subscript straight o straight t space equals space mv squared over 2
straight v squared space equals space fraction numerator 2 straight P subscript straight o straight t over denominator straight m end fraction
straight v proportional to space straight t to the power of 1 divided by 2 end exponent

Power Po = Fv
equals open parentheses straight m dv over dt close parentheses straight v
equals space mv dv over dt
Integrating space both space sides
integral straight P subscript straight o dt space equals integral mv space dv
straight P subscript straight o straight t space equals space mv squared over 2
straight v squared space equals space fraction numerator 2 straight P subscript straight o straight t over denominator straight m end fraction
straight v proportional to space straight t to the power of 1 divided by 2 end exponent

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