How Does Air Move in a Vacuum?

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A vacuum itself does not possess speed, as it is defined as the absence of matter. However, the air that is displaced to create a vacuum can have a speed associated with its movement. The rate at which a vacuum fills a container is contingent on how quickly air can exit the container. The discussion emphasizes that understanding vacuum dynamics involves focusing on the movement of air rather than the vacuum itself. Overall, the key point is that the speed of air leaving a container determines how quickly a vacuum can form.
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This might sound silly , but can a vacuum have a speed ?
 
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A vacuum isn't a thing; it's a lack of anything. The material that is displaced in order to create a vacuum will have a speed.
 
How fast can vacuum fill a container? The question is more correctly 'how fast can air leave the container?'
 
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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