Time Average Velocity is fine, but What is this “Space Average Velocity” ?
(I don’t have a Problem with the Question, but with the New “Space Average Velocity” Thing)
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Velocity can be expressed both in terms of time and in terms of the distance traveled, and then simply averaged over it.
If you’re wondering where this might be encountered, for example, when moving through a medium where the drag force is directly proportional to the first power of velocity, the work of this force can be written as: -k\, v_{\text{average over distance}}\, S.
(The translation may contain errors)
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What does “Averaging over Something” mean ?
also, When we Average over time, We kind of ensure that The Displacement remains the same, like, If a Particle starts from Zero velocity, and Moves for 5s with acceleration of 2ms^-2, we can see that displacement is 25m,
We can now see that the average velocity here will be 5m/s which when multiplied with Time gives the same displacement ~ 5*5 = 25m
In the similar way what remains constant for space averaged velocity ?
or do we just calculate space averaged velocity as we somehow need to have average Velocity as a function of Displacement ?
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“Averaging over something” is a mathematical concept — the formula you gave above (I recommend reading it in Calculus). In our case, “over something” refers to time or distance traveled. In any formula where appears \int v(s) ds , we can replace the integral with the average value multiplied by its increment; in the example above, this was the work.
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