What is the limit of average speed as time interval approaches zero?

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Discussion Overview

The discussion revolves around the concept of instantaneous speed and its relationship to average speed, particularly as the time interval approaches zero. Participants explore the implications of this concept within the context of physics and calculus.

Discussion Character

  • Conceptual clarification, Technical explanation

Main Points Raised

  • One participant questions the meaning of the statement that instantaneous speed is the limit of average speed as the time interval approaches zero.
  • Another participant suggests that over a sufficiently short time interval, speed does not change significantly, implying that instantaneous speed approximates average speed in such cases.
  • A later reply expresses appreciation for the clarification provided on the concept.
  • One participant introduces the idea that instantaneous speed is a result of classical physics and contrasts it with "contamechanics," suggesting a dichotomy in physics approaches.
  • Another participant notes that calculus was developed by Newton and Leibniz to address the concept of instantaneous speed.

Areas of Agreement / Disagreement

Participants generally agree on the relationship between instantaneous speed and average speed over small intervals, but there are differing views on the implications of classical physics and contamechanics.

Contextual Notes

Some statements rely on assumptions about the constancy of speed over short intervals and the definitions of classical physics versus contamechanics, which remain unresolved.

Bashyboy
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Hello,

I just sifting through the wikipedia article, concerning speed, for instantaneous speed and came across this bit explaining it: "...the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero." What specifically do they mean by this? If one could answer I would much appreciate it.
 
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Would you agree that over a short enough interval your speed doesn't change much? Thus your speed at anyone instant will tend to equal your average speed about that instant if you take a small enough interval.

Make sense?
 
Yes, that is very much more comprehendible. Thank you very much.
 
Instantaneous speed is achieved by today's world which is possible due to classical physics and contamechanics are the two types of physics. If classical physics results into positive then contamechanics results into negative.
 
Yes, Newton and Leibniz developed Calculus precisely to be able to talk about "instantaneous speed".
 

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