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

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In summary, the conversation discusses instantaneous speed and its definition as the limit of average speed as the duration of the time interval approaches zero. The concept is linked to classical and contamechanics physics and its relevance to calculus.
  • #1
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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  • #2
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?
 
  • #3
Yes, that is very much more comprehendible. Thank you very much.
 
  • #4
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.
 
  • #5
Welcome to calculus, Bashboy!
 
  • #6
Yes, Newton and Leibniz developed Calculus precisely to be able to talk about "instantaneous speed".
 

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

What is instantaneous speed?

Instantaneous speed is the rate at which an object is moving at a specific moment in time. It is the speed at a particular instant, rather than the average speed over a given distance.

How is instantaneous speed different from average speed?

Average speed is calculated by dividing the total distance traveled by the total time taken. Instantaneous speed, on the other hand, is the speed at a single moment in time and can vary throughout the motion of an object.

How is instantaneous speed measured?

Instantaneous speed can be measured using a speedometer or a stopwatch. It can also be calculated by measuring the distance an object travels in a very short time interval, such as one second, and then taking the average speed over that interval.

What is the unit of measurement for instantaneous speed?

The unit of measurement for instantaneous speed is the same as that for average speed - distance over time. In the SI system, this is meters per second (m/s).

Can instantaneous speed be negative?

Yes, instantaneous speed can be negative. A negative instantaneous speed indicates that the object is moving in the opposite direction of its positive direction, as defined by its velocity. For example, a car moving west with a velocity of 10 m/s would have a negative instantaneous speed when it is moving east.

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