Question

Formula of power in terms of force and velocity

Answer 1

Answer:

P = F.V

Explanation:

power in terms of force and velocity

power = force x velocity

P = F.V

Answer 2

$\huge{\bold{\underline{\underline{....Answer....}}}}$

$\huge{\bold{\underline{Given:-}}}$

Power = P.

Force = F.

Velocity = V.

Work done = W.

$\huge{\bold{\underline{Explanation:-}}}$

As we Know,

Power is defined as rate of doing work.

It is mathematically expressed as:-

$\large{\boxed{P = \frac{W}{T}}}$

Taking for a small interval of time

$\large{\bold{ P = \frac{dW}{dt}}}$

This is instantaneous power.

Derivation of Power in terms Of Force and Velocity.

As we know,

$\large{\bold{W = F.s ------(1)}}$

Taking instantaneous power.

$\large{\bold{P_{in} = \frac{dw}{dt}}}$

Substituting the work done formula from equation (1) in the instantaneous power.

$\large{ \implies P_{in} = \frac{d(F.s)}{dt}}$

As Force is constant it cannot be differentiated.

$\large{ \implies P_{in} = F. \frac{ds}{dt}}$

As $\large{ \frac{ds}{dt} = v}$

As rate of change of displacement = Velocity.

$\huge{\boxed{\boxed{P_{in} = F.v}}}$

So, the power is the product of Force and velocity applied on the object.