A particle of mass $m$ is lying on smooth horizontal table. A constant force $F$ tangential to the surface is applied on it. Find instantaneous power as function of time $t$ .

\frac{F^{2} t}{m}

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\frac{F^{2} t}{2 m}

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\frac{F^{2} t}{3 m}

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\frac{F^{2} t}{5 m}

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Solution

The correct option is A $\frac{F^{2} t}{m}$
Acceleration of particle due to constant force $F = a = \frac{F}{m}$
Thus velocity of particle at time $t = v = a t = \frac{F t}{m}$
Thus instantaneous power of particle at time $t = F v = \frac{F^{2} t}{m}$

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