On Wednesday, September 11, 2019 at 9:06:13 PM UTC+1, David Paste wrote:
because it is *per* second - the inverse, ie
second * second
1/x == x^-1 in this notation.
Compare, for instance, measuring carpet, which is in meters^2,
ie 'square meters', meters * meters, and not a minus in sight.
On Wed, 11 Sep 2019 13:06:10 -0700 (PDT), David Paste
'per second per second' is not 'seconds squared', it's 'per second
squared' (perhaps you meant that but omitted the 'per').
'one tenth' or 1/10 can be written 10^-1. Metres per second per second
can be written m/sec/sec or m/sec^2 or m.s^-2, the -ve sign indicating
'per' or 'one over' or division.
On Wed, 11 Sep 2019 13:06:10 -0700, David Paste wrote:
It's because it's /per/ second, indicating dividing. ms^2 would be metre-
second-seconds (i.e. distance times time times time), while acceleration
is ms^-2, metres per second per second, distance divided by time divided
Positive powers are multiplication, negative powers are division (or
"anti-multiplication"). x^2 is x*x, x^-2 is (1/x)/x. 2^2 is 4, 2^-2 is
If you multiply acceleration (ms^-2) by time (s, or s^1), you add the
powers - and get speed in ms^(-2+1) or ms^-1. If you divide acceleration
by time, you subtract the powers - and get jerk in ms^(-2-1) or ms^-3.
The same applies starting with distance, in m, or ms^0. Anything to the
power zero is 1, so m and ms^0 are the same thing. Divide by time and you
get ms^(0-1), ms^-1.
While all (or perhaps most) of the answers posted are correct, I don’t
think any quite get to the basic reason.
For that you need to look at the laws of indices.
4 = 2^2
1 = 2^0
1/2 = 2 ^ -1
1/4 = 2^ -2 = 1/(2^2)
I’ve use 2 for simplicity but the rules apply for other numbers.
Hopefully you can see the pattern.
If we substitute m for 2 then, in particular in the last line we get:
m^-2 = 1/(m^2) which is also 1/m * 1/m
The laws of indices ‘pop up’ in a number of places and can be very useful.
They are the basis of Logarithms, can be used to find HCF and LCMs, .......
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