- #1

- 439

- 156

## Main Question or Discussion Point

Stumbled on a potential pitfall that can arise if you combine Newton's overdot notation (for time-derivatives) with boldface/non-boldface notation for vectors/vector-magnitudes.

Say you have ##\textbf{v}## for velocity and ##\dot{\textbf{v}}## for acceleration. Speed is then ##v## (magnitude of velocity vector), but what does ##\dot{v}## mean? There are two possible interpretations:

1) the time-derivative of speed ##v##

2) the magnitude of acceleration ##\dot{\textbf{v}}##

In most contexts there's probably little risk of confusion (#2 can often be safely assumed). But one must be particularly careful in the one-dimensional case, when #2 is the absolute value of #1 and either quantity might prove useful. The danger there is a dreaded sign error.

Say you have ##\textbf{v}## for velocity and ##\dot{\textbf{v}}## for acceleration. Speed is then ##v## (magnitude of velocity vector), but what does ##\dot{v}## mean? There are two possible interpretations:

1) the time-derivative of speed ##v##

2) the magnitude of acceleration ##\dot{\textbf{v}}##

In most contexts there's probably little risk of confusion (#2 can often be safely assumed). But one must be particularly careful in the one-dimensional case, when #2 is the absolute value of #1 and either quantity might prove useful. The danger there is a dreaded sign error.