X*t, what is position multiplied by time?

[JLT]

TL;DR Summary

Area and slopes

So the pattern goes:

x(t)
v(t)
a(t)
jerk(t)

You can keep taking slopes of lines, and slopes of slopes - my questions is, what happens in the other direction- areas under curves and more areas under curves.

What is the area under the x(t) curve?

x*t, what is position multiplied by time?

 

[malawi_glenn]

TL;DR Summary: Area and slopes

What is the area under the x(t) curve?

Nothing of interest afaik.

 

[JLT]

Nothing of interest afaik.

Why are some physical quantities multiplied or divided by other quantities interesting, and other combinations not explored?

 

[Ibix]

Why are some physical quantities multiplied or divided by other quantities interesting, and other combinations not explored?

I don't think it's a case of "not explored". It's "nobody has found a use for it, so it doesn't get taught". Distance travelled per unit time is a useful quantity for stuff like predicting how long a whole journey will take given data on part of it. What would you use distance times time for?

 

[PeroK]

Why are some physical quantities multiplied or divided by other quantities interesting, and other combinations not explored?

Why does no one try holding a golf club by the head and hitting the ball with the handle?

Physics has an objective to explain natural phenomena. One important objective was to explan why planets move in ellipses. Newton developed the concepts and mathematics to achieve that objective. He wasn't just messing around aimlessly shuffling symbols on a bit of paper. Pure mathematicians do that!

 

[malawi_glenn]

Voltage times heat capacity, why has not anyone explored that?

 

[Nugatory]

Why are some physical quantities multiplied or divided by other quantities interesting, and other combinations not explored?

The interesting ones are the ones that are found to be useful in formulating the laws of physics or describing the properties of things. The others aren’t “unexplored”, they just haven’t been found to be useful.

We need $mv$ and $mv^2/2$ to predict the motion of a body so they’re interesting - so much so that we’ve given them names, “momentum” and “kinetic energy”. $mv^3$? We can calculate it, but why bother?

 

[Vanadium 50]

Why does no one try holding a golf club by the head and hitting the ball with the handle?

For some people it might help! At least it couldn't hurt.

Rutherford said "All science is either physics or stamp collecting." Attempting to name every possible derivative and antiderivative of positiion (especially since we know there is an infinite e number of such) sounds more like the latter.

 

[JLT]

I don't think it's a case of "not explored". It's "nobody has found a use for it, so it doesn't get taught". Distance travelled per unit time is a useful quantity for stuff like predicting how long a whole journey will take given data on part of it. What would you use distance times time for?

non-Euclidean mathematics was explored prior to applying the ideas to quantum mechanics.

If math is the language of the universe, something interesting should fall out of all of it.

time
position
mass

The above 3 are the building blocks if it all, and it just seems like all combinations of the above 3 should be explored - even if just for fun, even if it's just a purely mathematical exercise.

 

[PeroK]

The above 3 are the building blocks if it all, and it just seems like all combinations of the above 3 should be explored - even if just for fun, even if it's just a purely mathematical exercise.

There's nothing stopping you!

 

[Ibix]

The above 3 are the building blocks if it all

There are seven independent units defined in the SI. Time, length, mass, temperature, current, amount of substance, and luminous intensity.

just seems like all combinations of the above 3 should be explored - even if just for fun, even if it's just a purely mathematical exercise.

Knock yourself out. Random walks are a very inefficient way of getting to anything meaningful, though.

 

[malawi_glenn]

If math is the language of the universe, something interesting should fall out of all of it.

You can not draw that conclusion from that premise.

The above 3 are the building blocks if it all, and it just seems like all combinations of the above 3 should be explored

There are infiniteley many combinations.
And that is not how science is done.

This is starting to derail into a "personal theory" thread.

non-Euclidean mathematics was explored prior to applying the ideas to quantum mechanics.

Do you know why and how it was applied?

 

[Mark44]

Since the basic premise of this thread -- position times time -- is either nonsensical or of no use, take your pick, I'm closing this thread.