# Formula connecting Force and Power

Is there such formula? There probably is of course, but i would like a very concise description of how to derive it, in order to better understand myself. Thank you in advance.

• Here is a link to a website that includes much explanation: physicsclassroom.com/calcpad/energy. Notice that the original equation for work is a trigonometric function, because you must take into consideration the angle between the force vector and the displacement vector. Aug 29, 2015 at 13:04

Yes there is, first consider the original power formula

$P = w/t$

Now we know that work is equal to force.displacement (both vectors)

$P = (F.D)/t$

$P = F.(D/t)$

Displacement over time is velocity, so

$P = F.V$

Hence power can be stated as a dot product of the vectors force and velocity

Expanding the dot product

$P = FV\cos\theta$

Where $\theta$ is the angle between force and velocity, $F$ is magnitude of force, $V$ is magnitude of velocity.