Is Acceleration of Acceleration a Valid Concept in Physics?

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Discussion Overview

The discussion revolves around the concept of "acceleration of acceleration" in physics, exploring whether this idea is valid and how it might be mathematically expressed. Participants examine the implications of higher-order derivatives of motion, including terms like "jerk" and "jounce," and consider their physical significance and applications.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the meaning of "motion at an acceleration that is in a consistent change," seeking clarification on the mathematical representation of such a concept.
  • Another participant emphasizes that having a mathematical expression does not guarantee physical usefulness or meaning.
  • A later reply introduces the term "jerk," defined as the third derivative of displacement with respect to time, and notes its limited use in physics, particularly in engineering contexts like rollercoaster design.
  • The concept of "jounce," the fourth derivative, is mentioned as having even less application than jerk, suggesting that higher derivatives may have diminishing relevance.

Areas of Agreement / Disagreement

Participants express differing views on the validity and usefulness of higher-order derivatives in physics. While some acknowledge terms like "jerk" and "jounce," others question their practical significance.

Contextual Notes

The discussion highlights the uncertainty surrounding the physical interpretation of higher-order derivatives and their applications, with no consensus on their relevance in broader physics contexts.

Trepidation
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Acceleration is motion at a velocity that is in a consistent state of change, right? So...

v is in terms of m/s
a is in terms of m/s^2

So what is motion at an acceleration that is in a consistent change?

a^2 is in terms of m/s^3
or
a^2 is in terms of m/s^4
?

Is this 'acceleration of acceleration' ever used? Howabout acceleration of acceleration of acceleration, etc etc ad infinitum?
 
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Trepidation said:
Acceleration is motion at a velocity that is in a consistent state of change, right? So...

v is in terms of m/s
a is in terms of m/s^2

So what is motion at an acceleration that is in a consistent change?

a^2 is in terms of m/s^3
or
a^2 is in terms of m/s^4
?

Is this 'acceleration of acceleration' ever used? Howabout acceleration of acceleration of acceleration, etc etc ad infinitum?

Just because something has a mathematical expression doesn't mean it is automatically physically useful or meaningful.

Zz.
 
ZapperZ said:
Just because something has a mathematical expression doesn't mean it is automatically physically useful or meaningful.

Zz.

I know... The first part of my question was what the mathematical expression would be, and the second part was whether it would or would not be physically useful.
 
Trepidation said:
Acceleration is motion at a velocity that is in a consistent state of change, right? So...

v is in terms of m/s
a is in terms of m/s^2

So what is motion at an acceleration that is in a consistent change?

a^2 is in terms of m/s^3
or
a^2 is in terms of m/s^4
?

Is this 'acceleration of acceleration' ever used? Howabout acceleration of acceleration of acceleration, etc etc ad infinitum?

I don't think it's a^2 you want.

[tex]\vec{j} = \frac{d\vec{a}}{dt} = \frac{d^3\vec{x}}{dt^3}[/tex]

j is called 'jerk' (or sometimes 'jolt') and has units of m/s^3.

In physics jerk is rarely used, though in some areas of engineering (rollercoaster design would be the usual example) it is important.

The quantity:
[tex]\frac{d\vec{j}}{dt} = \frac{d^4\vec{x}}{dt^4}[/tex]
is often called 'jounce' and has even more limited use than jerk. Obviously you can keep on taking higher derivaives of dispalcement with respect to time without limit, but generally the higher the derivative the less it's use.
 
Thank you very much...
 

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