Wasn't sure where to put this question but I just have a little Q about units.
Say I want to know what units something will end up in, I know you can 'calculate' using just units (but without actual values assigned to the variables). Say I have a formula and one of the variables in it is squared - do I square the units of it, too?
Just as a bit extra, what happens when we take derivatives? For standard derivatives, say
, the units for these are typically
. For example, we have
, and the units of acceleration as stated earlier, were
. Why is this? Well, let's write our standard derivatives in 'English-speak'.
If I wanted to describe
, I would say "the rate of change of x, with respect to t". Or in other words, this describes "the ratio of the rates of change of x and t". In other words, it's like having
(which is really just a non-infinitesimal version of
, so this kinda makes sense), which would have units of
Now, when we take a higher derivative like
, this is really like
, so it's like "the ratio of the rates of change of (dx/dt) and t". In other words, we now have something like
, which can be treated like a fraction to give
, which explains the units for acceleration.
So yeah, hopefully this helps a bit.