Instantaneous Power: Velocity & Force Formula

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The formula for instantaneous power when given velocity and force is P = F * v, where P represents power, F is force, and v is velocity. Instantaneous power can also be derived by differentiating work done with respect to time. In general, power is defined as the work done divided by the time taken, expressed as P = W/t. Thus, when considering instantaneous conditions, power can be calculated as force multiplied by the instantaneous velocity. Understanding these formulas is crucial for analyzing the dynamics of moving objects.
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What is the formula for instantaneous power if I have velocity and force? And what is the formula in general?
 
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Instantaneous power is the power of a ny object at an instant.
if you differentiate work done w.r.t time it will be the instantaneous power. If the givn velocity is instantaneous the
power=F*v
as p=w.d/time taken =force*dis./time
 
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I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...

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