Question
Define power. Obtain an expression for it in terms of force and velocity.
✓
Answer
Power The rate of doing work is called power.
$\text{P}=^{\ \ \text{Lt}}_{\Delta\text{t}\rightarrow0}\frac{\Delta\text{W}}{\Delta\text{t}}=\frac{\text{d}\text{W}}{\text{d}\text{t}}$
$=\frac{\text{d}}{\text{d}\text{t}}(\vec{\text{F}}.\vec{\text{S})}=\vec{\text{F}.}\frac{\text{d}\vec{\text{s}}}{\text{dt}}$
$\text{P}=\vec{\text{F}.}\vec{\text{V}}$
$\Rightarrow\text{P}=\text{Fv}$
$\text{P}=^{\ \ \text{Lt}}_{\Delta\text{t}\rightarrow0}\frac{\Delta\text{W}}{\Delta\text{t}}=\frac{\text{d}\text{W}}{\text{d}\text{t}}$
$=\frac{\text{d}}{\text{d}\text{t}}(\vec{\text{F}}.\vec{\text{S})}=\vec{\text{F}.}\frac{\text{d}\vec{\text{s}}}{\text{dt}}$
$\text{P}=\vec{\text{F}.}\vec{\text{V}}$
$\Rightarrow\text{P}=\text{Fv}$
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