Question about notation on derivatives

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Homework Help Overview

The discussion revolves around the notation used for derivatives in physics, particularly in the context of acceleration and velocity. Participants are exploring how to correctly express these derivatives using dot notation and other forms of notation.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning whether it is necessary to include additional context when using dot notation for derivatives, such as specifying what the variables represent. There is also a discussion about the appropriateness of using different notations for derivatives, including dot notation versus prime notation.

Discussion Status

Some participants have provided insights into the historical context of the notation and its implications, while others are seeking clarification on the correct usage of these notations. Multiple interpretations of how to express derivatives are being explored, indicating a productive exchange of ideas.

Contextual Notes

There is mention of the challenges associated with using dot notation in written form, particularly in relation to formatting in LaTeX. Participants are also considering the conventions of different notational systems, such as Newton's and Leibniz's approaches.

GreenPrint
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Homework Statement


If I'm asked to find the acceleration at t=2 s I can just put the X with two dots on top of it parentheses(2 s)?
X(2) = what ever I calculate it being equal to

that's all I have to put right the X with two dots indicated the derivative of x( distance) the two dots indicating the second derivative acceleration

If I wanted to show like I don't know the first derivative of volume with reference of time I can just put V with a dot above it right i don't have to put V = volume or X = displacement next to it right?

Homework Equations





The Attempt at a Solution

 
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or do I have to put the v with a dot above it to indicate the first derivative of velocity with parentheses (2) next to it instead right becaues that would be more correct?
 
GreenPrint said:

Homework Statement


If I'm asked to find the acceleration at t=2 s I can just put the X with two dots on top of it parentheses(2 s)?
X(2) = what ever I calculate it being equal to

that's all I have to put right the X with two dots indicated the derivative of x( distance) the two dots indicating the second derivative acceleration

If I wanted to show like I don't know the first derivative of volume with reference of time I can just put V with a dot above it right i don't have to put V = volume or X = displacement next to it right?
I have no idea what you're trying to get across in about half of what you wrote.

The dot notation for derivative is due to Newton, who always used it to mean derivative with respect to time. Another notation uses a prime symbol (') to indicate a derivative (not necessarily with respect to time).

Leibniz's notation uses differentials, with dy/dt meaning the derivative of y with respect to t.

Since it's difficult to put one or more dots above a letter without doing something fancy in LaTeX, why bother with the dot notation?
 
GreenPrint said:
or do I have to put the v with a dot above it to indicate the first derivative of velocity with parentheses (2) next to it instead right becaues that would be more correct?

v(t) represents the velocity at an arbitrary time t.
v(2) represents the velocity at time 2, in whatever time units are being used.
v'(t) is the derivative of the velocity with respect to t (i.e., the acceleration) at an arbitrary time t.
v'(2) is the derivative of the velocity with respect to t (i.e., the acceleration) at time 2.
 
Thanks I just wanted to make sure...
 

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