SOLUTION: Hi,
I can't get why an acceleration per second per second is named per second squared, usually in math we use it to multiply a number by its own number so its like squaring the nu
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Question 802783: Hi,
I can't get why an acceleration per second per second is named per second squared, usually in math we use it to multiply a number by its own number so its like squaring the number, but in acceleration its obvious that you don't multiply the time you accelerate by the same time, you only add for every second the amount added in the second before?,
Thanks for your help,
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let's say that at time 
you are moving at 
and your acceleration is 
. Now, what is your velocity at 
if 
? Well, 
, so putting in the numbers AND the units we get \ =\ 4\text{m/sec}\ +\ 1\text{m/sec^2}*1\text{sec})
. Now, when you do the actual arithmetic, units in a numerator (as in the time) cancel units in a denominator (like one of the factors of 'sec' in acceleration).
Another way to look at it is that acceleration in meters per second squared times time in seconds has to equal velocity in meters per second. Half of acceleration in meters per second squared times time in seconds squared is distance in meters.
It makes a lot more sense when you do it with the calculus (this for constant acceleration):
\ =\ \int\,a\,dt\ =\ at\ +\ v_o)
\ =\ \int\,(at\ +\ v_o)dt\ =\ \frac{1}{2}at^2\ +\ v_ot\ +\ s_o)
And then back the other way:
\ =\ \frac{ds}{dt}\ =\ at\ +\ v_o)
\ =\ \frac{d^2s}{dt^2}\ =\ \frac{dv}{dt}\ =\ a)
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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