Sign problems with vectors, how can we "resolve" this....

[etotheipi]

For example, the equation $v=v_o+at$ that is used in the study of one-dimensional motion should be written, for example, as $v_x=v_{ox}+a_xt$ to make it explicitly clear that we are talking about vector components and not vector magnitudes. Of course, that introduces an extra layer of complexity for students who are already struggling to understand things.

Just one further thought; it definitely seems clearer to insert the subscripts in order to distinguish components like $v_{x}$ from magnitudes like $v$, however when I look at even some undergraduate level lecture notes it seems the latter is used quite often also for the signed component - the notation clash @robphy referred to.

I wonder whether in your opinion it would be worth getting into the habit of writing out the subscripts (which is what I'm sort of inclined to start doing, purely for clarity's sake) even for one dimensional motion?

The downside is evidently brevity, and if the system perhaps requires more than one coordinate system when solving (e.g. pulleys) we might need to start putting in $x'$'s and $y'$'s et cetera which takes a little longer. Though it arguably reduces any ambiguity.

What do you think?

 

[Mister T]

I wonder whether in your opinion it would be worth getting into the habit of writing out the subscripts (which is what I'm sort of inclined to start doing, purely for clarity's sake) even for one dimensional motion?

The downside is evidently brevity, and if the system perhaps requires more than one coordinate system when solving (e.g. pulleys) we might need to start putting in x′x′x''s and y′y′y''s et cetera which takes a little longer. Though it arguably reduces any ambiguity.

What do you think?

You can look at what Randy Knight does in his introductory textbooks. He uses a subscript of $s$ to stand for any component in general, and then replaces $s$ with $x$ for horizontal motion and with $y$ for vertical motion. Sounds neat, but we also have to deal with inclined planes.

Since you understand the role played by the subscripts it's probably a good idea for you to insert them. I have tried teaching it both ways, and prefer to leave the subscripts off at the beginning. They can be inserted later on in the introductory course when the study of two-dimensional motion begins.