If a force \(F\) is applied on a body and it moves with a velocity \(v\), the power will be

If a force \(F\) is applied on a body and it moves with a velocity \(v\), the power will be
  1. \(F \cdot v\)
  2. \(\frac{F}{V}\)
  3. \(\frac{F}{v^2}\)
  4. \(F \cdot v^2\)

Solution

We know that, power is given as \(\begin{aligned} & P=\frac{d W}{d t}=\frac{d}{d t}[F \cdot s] \quad[\because W=F \cdot s] \\ & =F \cdot \frac{d s}{d t} \quad \text { [For constant force } F \text {] } \\ & \Rightarrow \quad P=F \cdot v \quad {\left[\because v=\frac{d s}{d t}\right]} \\ \end{aligned}\)

Asked in: AP EAMCET 2020 (18 Sep Shift 1)

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