The work done by a force \(\vec F\) for a displacement \(d \vec r\) is
W= \(\int \vec F. d\vec r\) .................(i)
Left hand side of the equation (i) can be written as
Right hand side of the equation (i) can be written as dt
Substituting equation (ii) and equation (iii) in equation (i), we get
This relation is true for any arbitrary value of dt. This implies that the term within the bracket must be equal to zero, i.e.,
Hence power P = \(\vec F. \vec v\)
