The unit to measure speed is m/s which in a straightforward manner implies that x metres is covered per second however the unit for acceleration is m/s^2 which is kind of making it difficult to understand how it works..
I had this thought in the middle of a physics test and have been pondering ever since. Would be great if someone could eli5.
In: Physics
Acceleration is a change in velocity (very similar to speed). If you speed up from from 0 m/s to 1 m/s in one second, then you’ve accelerated (1 m/s) *per second*.
So if you were accelerating at 10 m/s *per second* for 10 seconds, you’d wind up traveling at 100 m/s by the end.
Acceleration can also be written as (m/s)/s. To help visualize it, let’s use an acceleration of 1 m/s^(2). Again, we expand that to 1 (m/s)/s. What this means is that, for every second that something is accelerating, 1 m/s is added to the speed.
After the first second, the object is going at 1 m/s. After the second second, it’s going 2 m/s. After the third, 3 m/s, etc.
It’s functionally measuring how much faster you’re getting faster. If acceleration is, say, 2m/s^2, on second 1 you’re going 0m/s, on second 2 you’re going 2m/s, on second 3 you’re going 4m/s, on second 3 you’re going 6 m/s and so on.
It just means you’re going 2 m/s faster each second.
Oh they just smooshed it all together.
They measure speed in m/s. That is easily understood, a change in measurement per time. In this case the process is motion, we measure meters of distance, so it’s m/s.
Acceleration is speed with which the speed changes. Again, it is speed, again a change of measurement per time.
Only this time the measurement is m/s, so you get (m/s)/s. Like, in a second my speed changed from 2m/s to 5m/s, so my acceleration is 3(m/s)/s.
When a unit has relations like division and multiplication, you can do to it everything that algebra allows to do with analitic expressions. So, they do a very basic thing.
Since it’s a meter divided by a second, and all of that is divided by a second again, you can multiply those seconds and get s^2.
You can verify it in your head if you imagine specific numbers. Let’s say (32/2)/2. You can divide 32 by two and then again, so you get 8. Or you can do 32 divided by 2^4, which is again 8.
Got it. Thanks for the help
The way you say m/s^2 is “per second per second”, which makes it easier to understand:
If something is accelerating at a rate of 1 meter per second per second, they are getting 1 meter per second faster every second.
If velocity is distance change per time, or meters per second
Then acceleration is velocity change per time, or meters per second per second, or meters per second squared.
Velocity or speed is measure in distance over time v = (d/t)
Acceleration is measured in velocity over time a = (v/t)
Substitute the equation of velocity to the equation of acceleration and simplify gives you:
a = (d/t)/t = d/t²
Instead of writing it, try saying it. Your speed is in metres per second; you travel a certain distance every second.
Your acceleration is in metres per second per second; your speed changes by a certain amount every second.
Velocity (m/s – x metres per second): Every second, your position changes by x metres in a given direction.
Acceleration (m/s^2 – x metres per second, *per second*): Every second, your velocity in a given direction changes by x metres per second. – “Metres per second squared” is basically just a shorthand.
So if your velocity is currently “7 metres per second” (7 m/s), and your acceleration in the same direction is “2 metres per second, per second” (2 m/s^2 ), that 7 will grow by 2 every second. After 1 second, your velocity will be 9 m/s. After 2 seconds, 11 m/s. And so on.
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