XPost: sci.math   
   From: PointedEars@web.de   
      
   The 'nym-shifting troll trolled as "Wayne Timerbaev":   
   > Paul B. Andersen wrote:   
   >> Den 28.01.2026 20:04, skrev Paul B. Andersen:   
   >>> Hint: d²v/dt² = 10 m/s²   
   >>   
   >> Should be:   
   >> Hint: dv/dt = 10 m/s²   
   >   
   > idiot, you have to put the time in it, to find the speed, wrt the place   
   > the time is starting, if not offset.   
      
   Since the acceleration is the time derivative of velocity, from the   
   fundamental theorem of calculus follows that, if the motion is along a   
   straight line, the speed is obtained by integration of the magnitude of the   
   acceleration over time:   
      
     v(t) = ∫ dt [dv/dt](t) = ∫ dt a(t).   
      
   If the acceleration is constant over time, too, the integral is trivial to   
   calculate:   
      
     v(t) = ∫ dt a = a ∫ dt = a t + C; C = const. (wrt. t)   
      
   One can see then that the constant of integration is C = v(0).   
      
   But that is precisely the point that Paul B. Andersen was making, and that   
   the 'nym-shifting troll here missed:   
      
   The initial speed is unknown as well as the time t = 0 at which the   
   acceleration began; moreover, the initial speed depends on the choice of   
   rest frame as all speeds are (measured) relative (to something else).  So it   
   is not possible to tell the speed of an object merely from the magnitude of   
   its (proper) acceleration.   
      
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   PointedEars   
      
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