"Accelerations" as higher order derivatives

[E Rinella]

TL;DR Summary

Physical interpretations of higher order derivatives of time: velocity, acceleration, etc. ...

In physics, velocity (speed) is the "change of position (spacial location) per change of time" and acceleration is the "change of velocity per change of time". Mathematically this is first and second derivative. Do further derivatives exist that correspont physical quantities like "change of acceleration per change of time" ... etc.?

 

[Baluncore]

Yes.
Position, Velocity (speed), Acceleration, Jerk, Snap (jounce), Crackle, Pop.
https://en.wikipedia.org/wiki/Jerk_(physics)

 

[sophiecentaur]

TL;DR Summary: Physical interpretations of higher order derivatives of time: velocity, acceleration, etc. ...

Do further derivatives exist that correspont physical quantities like "change of acceleration per change of time" ... etc.?

There's no limit to how many orders of derivative - because it's Maths. But practically, you can easily 'see' how you can go further than acceleration (second derivative of time) because acceleration is proportional to Force and force can easily vary as an object changes its position. The force from a rubber band goes up as you stretch it. For small displacements about a position where the rubber is stretched 'a bit' the force will be proportional to the displacement (there's a third order of derivative) but rubber is very non-linear so the force won't be truly proportional to the displacement so that will take you into a fourth derivative of time. You can go further when the experiment is affected by even more variables.
Robert Hooke could be turning in his grave about this but I'd bet he thought about this a lot so maybe he wouldn;t have been too surprised the way things have gone. Round about his time (The Enlightenment) Maths was being developed and that helped with descriptions of processes where nothing was straight 'proportional' and describing that sort of thing without Maths could be very difficult.

 

[E Rinella]

Yes.
Position, Velocity (speed), Acceleration, Jerk, Snap (jounce), Crackle, Pop.
https://en.wikipedia.org/wiki/Jerk_(physics)

Yes, thank you. While "Jerk" is described, what are the physical meaning and applications of "higher order accelerations"?

 

[Vanadium 50]

what are the physical meaning and applications of "higher order accelerations"?

There really aren't any. Just names. Because people demand names.

 

[sophiecentaur]

Those ‘names’ you want are short for ‘rate of change of rate of change of rate of change of etc…..’. Going further than a second derivative is easier described in Mathematical expressions. But that seems to be a general principle that Maths is a useful short form to describe most of Physics and Engineering.
Which is easier to communicate: s/t or metres travelled in 20 seconds?

 

[Baluncore]

While "Jerk" is described, what are the physical meaning and applications of "higher order accelerations"?

They do not need to have a physical meaning, and you will probably never need to use them all. They will have a different meaning, in each field of application.

Each is used in turn, to remove a step-discontinuity, to push it one further domain away, from where you are working with continuous functions. If you need them for your applied mathematics, they are available to you.

For me today, they are conveniently there, simply as an answer to your original question.

 

[sophiecentaur]

They do not need to have a physical meaning, and you will probably never need to use them all.

A point worth mentioning is that there are no practical situations in which the relationship between two variables is linear over the whole range. Speed is never uniform and nor is acceleration; there are always deviations from the straight line curve. Those higher order accelerations are always there.

 

[E Rinella]

Those ‘names’ you want are short for ‘rate of change of rate of change of rate of change of etc…..’. Going further than a second derivative is easier described in Mathematical expressions. But that seems to be a general principle that Maths is a useful short form to describe most of Physics and Engineering.
Which is easier to communicate: s/t or metres travelled in 20 seconds?

Yes, absolutely with you. But there are no physical meaning and applications of thus further derivatives, right? They are just mathematical constructs?