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

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The discussion centers on the concept of instantaneous speed, defined as the limit of average speed as the time interval approaches zero. It emphasizes that over very short intervals, speed remains relatively constant, making instantaneous speed closely align with average speed. The conversation highlights the foundational role of calculus, developed by Newton and Leibniz, in understanding this concept. Classical physics is mentioned as a framework for positive outcomes, while contamechanics is noted for its negative implications. Overall, the thread clarifies how calculus enables the precise discussion of instantaneous speed.
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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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