Formula of power in terms of force and velocity

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Formula of power in terms of force and velocity

Answered by admin @


\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.


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