An actual meaning of instantaneous velocity

[Clockclocle]

TL;DR Summary

I this a true way of understanding of instantaneous velocity??

After a year of thinking about instantaneous velocity. I think that this notion is no more than a mathematic coincidence when mathematician tried to find the tangent of curve. The only definition of velocity that make sense is $\frac{\Delta x}{\Delta t}$, this proportion is a quantity that show how much the object move after a certain of time.

If we let the object to have a velocity at each instant, let say a man is moving at 500m/s 10 second after we press the clock, that mean that if he do not push the pedal after this instant he will move 5000 m after 10 seconds. However, he might push the pedal since there are many other cars, so the velocity at each time will no the same because if we look at him from the road he will be slowdown.

The first case is easy to find the whole road he ride after 10 second by multiply 500m/s with 10s we get 5000m, the latter case is more complicated, but when we graph the function of each 2 scenarios, the problem of finding the whole distance will the as same as calculate the area under the graph then we use the integral from mathematical analysis. I think that the notion of average velocity is misleading, the way it represent look like it depend on the function of distance, while it is just a quantity to show how much the distance change after a certain time. Finally, we should not teaching average velocity, there is only one true velocity that is instantaneous velocity which make sense

 

[erobz]

You can't measure instantaneous velocity. It is a theoretical construct. Every real measurement of velocity is an average velocity.

 

[pines-demon]

You can't measure instantaneous velocity. It is a theoretical construct. Every real measurement of velocity is an average velocity.

Well you kinda can, Doppler measurements allow it does it not?

 

[erobz]

Well you kinda can, Doppler measurements allow it does it not?

Its is a philosophical absolute what I'm talking about? clock starts, position of something noted. clock stops again new position of that something noted. Velocity can be computed...its an average in practice.

$$ \vec{v} = \lim_{ \Delta t \to 0} \frac{ \Delta \vec{x}}{ \Delta t} $$

That whole limit operation is truly unphysical in my opinion. The physics of our consciousness is "filling in the gaps" for the "instantaneous" velocity. If instantaneous velocity is computed, it's not done until we have assumed (consciously) some functional form (other than linear - average) between endpoints. Is that controversial?

 

[russ_watters]

Its is a philosophical absolute what I'm talking about? clock starts, position of something noted. clock stops again new position of that something noted. Velocity can be computed...its an average in practice.

In practice it's an average for certain methods of measuring it. For other methods it isn't, but whether those methods "count" because they might be considered proxies, not direct measurements of speed is probably a matter of opinion/philosophy.

 

[erobz]

In practice it's an average for certain methods of measuring it. For other methods it isn't, but whether those methods "count" because they might be considered proxies, not direct measurements of speed is probably a matter of opinion/philosophy.

Well, its seems to be the argument of the OP in a philosophical sense - or rather to avoid that term -is axiomatic the better? Although I didn't find the OP's post easy to follow.

 

[Dale]

The only definition of velocity that make sense is $\frac{\Delta x}{\Delta t}$, ... I think that the notion of average velocity is misleading, ... we should not teaching average velocity, there is only one true velocity that is instantaneous velocity which make sense

I really don't understand the above. $\frac{\Delta x}{\Delta t}$ is average velocity. So first you say that average velocity is the only definition of velocity that makes sense. Then you say that it is misleading and we should not teach it. And then you say only instantaneous velocity makes sense.

For clarification: average velocity is $\frac{\Delta x}{\Delta t}$. Instantaneous velocity is $\frac{dx}{dt}$. The two are related by $\frac{dx}{dt}=\lim_{\Delta t \rightarrow 0}\frac{\Delta x}{\Delta t}$