From: poutnik@privacy.net   
      
   Dne 21/01/2018 v 10:55 augustin.coppey@gmail.com napsal(a):   
   >   
   > Explanation:   
   >   
   > If we look at the speed formula v = (x2-x1)/(t2-t1) as a transfer   
   > function with inputs and outputs (as in systems theory), we can see that   
   > the time series v(t) will always lag the time series x(t) by (t2-t1)/2   
   > no matter what the scale or distance is.   
   >   
   > This is because the speed as calculated is only valid (if at all) as an   
   > average speed between the 2 positions, and therefore only defined at the   
   > average position between the 2 measurement points. Placing the speed   
   > anywhere else but at the average position has little to no physical   
   > meaning (unless we have a higher sampling resolution to locate the point   
   > more precisely, and pushing this to the extreme, yes we do end up in   
   > quantum mechanics and Planck constant - but that is measurement   
   > resolution, not an absolute uncertainty principle).   
   >   
   > Example: even on a scale of meters and seconds, I cannot know precisely   
   > **by measurement** the speed and position of a slow moving object if I   
   > only have samples at each meter. I will know exactly the position when   
   > the object crosses the meter marker - but the calculated speed will be   
   > only an average speed between the last 2 markers, valid at the average   
   > location between the 2 markers. It is definitely NOT the speed when   
   > crossing the marker (simple proof: if the object is accelerating)   
   >   
      
   What you describe is a formula for an average speed, not speed.   
      
   Furthermore, the average speed is not at all defined   
   for the middle position between the markers,   
   or any other particular point.   
      
   The point, where the speed=average speed is known to exist,   
   but its placement is generally unknown.   
      
   Speed can be measured point-like by different means,   
   e.g. from the Doppler effect.   
      
   --   
   Poutnik ( The Pilgrim, Der Wanderer )   
      
   A wise man guards words he says,   
   as they say about him more,   
   than he says about the subject.   
      
   --- SoupGate-Win32 v1.05   
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