Question

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

t²P_o

t^1/2

t^-1/2

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

Solution

t^1/2

Power P_o = 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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Work, Energy And Power

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Does the body at rest possess energy?

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For Daily Free Study Material Join wiredfaculty

Work, Energy And Power

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

Some More Questions From Work, Energy and Power Chapter

Does the body at rest possess energy?

By eating two apples, a person starts pushing the wall of room. If food value of apple is 100 calories per apple, how much work he will do in pushing the wall in one hour?

A man is rowing upstream and is at rest w.r.t. shore. Is he doing work w.r.t. shore?

Is frictional force conservative?

What is the work done by gravitational force in taking the mass m with constant velocity through height h?

A mass is tied with a string and whirled in horizontal circle. What is the work done by tension force?

Does the work done by force depend upon the velocity at that instant?

What is the work done by man against gravity when he is carrying a load on his head and walking on the horizontal road?

Are all central forces conservative?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation