Question

The instantaneous power in terms of force $F$ and instantaneous velocity $v$ is

• A. $P=F \cdot t$
• B. $P=F \cdot v$
• C. $P=F \cdot v^{-1}$
• D. $P=F \cdot v^{-2}$
• E. $P=F \cdot v \cdot t^{-1}$

Answer 1

Answer: (B)

Instantaneous power, $P=\displaystyle\lim _{\Delta t \rightarrow 0} \frac{\text { Work done }}{\text { Time taken }}$
$=\left|\frac{d W}{d t}\right|$
As,
$d W=F \cdot d r $
$ \Rightarrow \quad P=F \cdot \frac{d r}{d t}$
Again, $\frac{d r}{d t}=v$, instantaneous velocity
Therefore, $P=F \cdot v=F v \cos \theta$