A constant force F acts on a body of mass m i | vedclass

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(D) The power $P$ delivered by a force $F$ is given by the formula $P = F \cdot v$,where $v$ is the velocity of the body.Since the force $F$ is consta

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(D) The power $P$ delivered by a force $F$ is given by the formula $P = F \cdot v$,where $v$ is the velocity of the body.Since the force $F$ is constant,the acceleration $a$ of the body is also constant,given by $a = F/m$.Starting from rest $(u = 0)$,the velocity $v$ at any time $t$ is given by $v = u + at = 0 + (F/m)t = (F/m)t$.Substituting this into the power formula,we get $P = F \cdot ((F/m)t) = (F^2/m)t$.Since $F$ and $m$ are constants,$P \propto t$.This represents a linear relationship between power $P$ and time $t$,which is a straight line passing through the origin.Therefore,the graph showing a linear increase of power $P$ with time $t$ is correct,which corresponds to option $D$.

$A$ constant force $F$ acts on a body of mass $m$ initially at rest. Which of the following graphs correctly represents the variation of the power $P$ developed with time $t$?

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