Question about notation on derivatives

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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?

 

[Mark44]

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?

 

[Mark44]

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.

 

[GreenPrint]

Thanks I just wanted to make sure...