Derive the formula for power delivered to a body. Prove that instantaneous power delivered to a body is given by the product of force and velocity of the body

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Solution

$D e a r S t u d e n t, P o w e r i s d e f i n e d a s t h e w o r k d o n e i n u n i t t i m e o r t h e e n e r g y u s e d i n u n i t t i m e . H e n c e, P o w e r = \frac{W o r k}{t i m e} = \frac{W}{t} o r, P o w e r = \frac{E n e r g y}{t i m e} = \frac{E}{t} W e t a k e, P = \frac{W}{t} . . . . . . . . . . . . . (1) W o r k d o n e, w = F \times s w h e r e, F \to A p p l i e d f o r c e s \to D i s p l a c e m e n t o f t h e b o d y E q u a t i o n (1) b e c o m e s, P = \frac{F \times s}{t} = F \times v (v e l o c i t y, v = \frac{s}{t}) H e n c e, P o w e r = F o r c e \times V e l o c i t y R e g a r d s .$

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