Question

Show that power is equal to dot product of force and velocity

Answer 1

Derivation :

• Power output is defined as the rate of doing work with respect to time.

$Power = \dfrac{Work}{time}$

• Work can be expressed as the scalar product of force vector and displacement.

$\implies Power = \dfrac{ \vec{F }. \vec{d }}{time}$

$\implies Power = \dfrac{ F \times d \times \cos( \theta) }{time}$

• (d/time) can be written as velocity .

$\implies Power = F \times v \times \cos( \theta)$

$\boxed{ \implies Power = \vec{F}. \vec{v}}$

[Hence derived]

• So, power can be written as dot product of force and velocity vectors.

Answer 2

Answer:

we have,

power=work done/time

=> power=Fdcosθ/time

=>power=Fvcosθ