# Getting back into math

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I spent 2 years in college in a major with no math. Now I switched to physics and I am trying to relearn a lot. It seems I forgot almost everything. I am currently in a college trig course and chemistry, and I understand just fine. But there is some notation I do not remember the significance of kg^-1 m/s^-2. In chemistry, there are lots of units like kg^-1 m/s^-2. The ^ is used to designate superscript. I know that is like kg per meter per second per second (this is just some units I threw togather), but why does it use negative numbers? I cannot remember. I also do not remember how to deal mathematically with things like meters per second per second, even though I know the meaning. Like in calculating distance of a falling object,it is (1/2)(9.81)(t^2) or something like that, but how is it derived and why 1/2. I can do the math fine for chemistry because I understand the concepts of chemistry and can cancel my units properly, but I do not remember this notation. Can anyone refresh my memory?

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x^-2 means 1/(x^2). Therefore ms^-1 means m/s. Meters per second per second is ms^-2.

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Quote:
 Original post by WitchcravenLike in calculating distance of a falling object,it is (1/2)(9.81)(t^2) or something like that, but how is it derived and why 1/2.

u = starting velocity, v = end velocity, s = displacement, t = time

average velocity = (u + v)/2
average velocity = s/t
=>
s/t = (u + v)/2
=>
s = t((u + v)/2)
=>
v = u + at
so:
s = t((u + u + at)/2)
=>
s = ut + (1/2)(a)(t^2)

For a falling object, a = g = 9.81.

Hope that helps.

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Negating an exponent is equivalent to reciprocating the base:

x^-n = 1/(x^n) = (1/x)^n

As you can see, this operation is self-inverse:

x^n = x^--n = 1/(x^-n) = 1/(1/x^n) = x^n

I'm not sure if it was a typo or not, but your first example is actually second-second-metres per kilogramme. Either / or ^-n notation is fine, but they shouldn't be mixed and parenthese should be used where necessary. Your example features '/s^-2' which is the same as 's^2' as the two reciprocals cancel out.
I imagine the confusion came from recalling the base SI units of energy, the Joule = kg.m²/s².

When manipulating quantities with units, a few good rules will go far:

Units should be manipulated just like fractions.
Whatever operation is done to the values should also be done to their units.
In a sensible formula, all terms (i.e. tokens separated by a +, - or =) should have the same units.

Check this third rule every so often during your work. If it fails, you have probably made an error somewhere.

Rebooted's derivation was spot on, but just to clarify: That formula is valid only for particles under constant acceleration. In the case you quoted, this constant acceleration is acceleration under the earth's surface gravity where the varable 'a' is taken as the constant 'g = -9.81'.

Regards

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