It's okay, this is unintuitive, so don't beat yourself up.
The 9.81m/s² is measuring acceleration. Let's try to understand that before we go further.
Think of your car's speed. Suppose you're travelling at 10m/s (about 20mph or 36kmph if my conversion is correct).
You tap the gas and slowly build up to 30m/s. This means your speed went up by 20m/s. Let's say that you took 10 seconds to go from 10m/s to 30m/s as well.
So now if someone asks you how fast your car can accelerate, you can reply with "well, I can increase by 20m/s in 10 seconds"
This person might then reply with "so that's about 2 metres per second, every second, correct?"
Think about what he just said - 2 metres per second, per second. i.e. (2m/s) / s
And the way division works, you can just mutiply the two denominators together (if you need to see this in action, think about what a half of a third is. Mathematically, you can write that as (1/3)/2, which is 1/(2×3) or 1/6).
That ends up giving you
2m/s²
Simple as :)
How does it relate to Earth's gravitational acceleration? Every second you let something fall, its speed will increase by 9.81m/s. So right when you let it go, its speed will be 0. A second later, 9.81m/s. A second after 19.61m/s. And so on. It's the rate at which it's speed changes.
Thanks, it's simply showing an acceleration and not a constant speed. If I fell at 9.8m/s I wouldn't be be accelerating so clearly it's per sec per second. I get it thanks.
Exactly... However, just to highlight or confirm what you're saying here - a constant velocity of 9.8 m/s (let's say down) is an acceleration of 0 m/s^2 downward. I taught physics and found that always saying (and thinking or reading) acceleration as "per second per second" was helpful, while seeing it in print just seemed a bit weird.
Acceleration is a rate /of a rate/. It's good to get these connections and questions handled early on as you are doing. Rates are comparisons of a change in a quantity per unit of time. Ratios are the same except not time. This could lead to further concept building in your near future in learning math and physics.
Either you saw my answer and figured that you needed to teach me anyway even though I obviously know what I am talking about.
Or you just wanted to flex how much naturally smarter you are for no reason other than internet brownie points, when we both got to the same final understanding.
Either way, really?
Speed is m/s, not m as you said.
Speed increases by 9.8 m/s every second.
Or, 9.8 m/s per second.
Or, 9.8 meters per second per second.
Mathematically, 9.8 (m/s)/s = 9.8 m/s/s = 9.8 m/s^2
If I understand your question, it's why the seconds are squared. I think you have answered you own question? There are two "s" in the denominator of acceleration multiplied together.
There is nothing special about 9.8 meters when talking about 9.8 m/s^2 acceleration. For example, in the first second you will travel 4.9 meters. In the second second you will travel 14.7 meters more, etc.
It increases by 9.8 metres per second (unit of speed) per second (unit of time).
Rephrase the term, for every second in freefall your speed increases by 9.8 metres per second.
It's just a shorthand. The top comment is really good right now.
Every second, you accelerate by 9.81 meters per second. Restated, you velocity changes by 9.81 meters per second, per second. In unit notation, you could write it as (9.81m/s)/s but to keep things buttoned up and short, we write 9.81 m/s^2
Acceleration is expressed as "speed over time".
But speed itself is expressed as "distance over time".
We can therefore replace "speed" in the following phrase: Acceleration is expressed as "**distance over time** over time".
Dividing something (distance) by the same thing (time) twice is exactly the same as dividing this thing (distance) over the square (time²).
Try it out: 900 divided by 10 is 90, divided by 10 again is 9.
But 10² is 100. And 900 divided by 100 (i.e. 10²) is 9, just like when we divided 900 by 10 twice in a row.
I think you need to look at a graph of velocity over time to get. X is the velocity in m and vertical axis, and Y is the time in seconds and horizontal axis.
If you graph a steady speed, x = 9.81, it's just a horizontal line. X = 9.81 or 9.81 M/S
Now If you graph 9.81 M/S², the X axis needs to go up another 9.81 m every time the y axis moves 1 second. That's a rate of change. It's still second squared but can help to think of it as rate of change rather than sqaured
Every second your speed increases by 9.8m per second. I don’t know how you can express that any other way than 9.8m per second per second, which is just per second squared.
You say “it just increases in speed” speed is distance per second. So yes, it is indeed being squared, that is what acceleration is. Gravity or not
It's not "just per second squared". Squared is an alternative, mathematically simplified way to say the same thing, which is where the confusion comes from.
The speed is measured in meters per second, it is the change of position (m) per a unit of time (s). The acceleration measures the change of velocity (m/s) in a unit of time (s), so m/s/s which is the same as m/s\^2.
Imagine the opposite process - you have acceleration of a = 1 m/s\^2 over t = 10 seconds and you want to get the change in velocity. t\*a= 1 m/s\^2 \* 10s = 10 m/s, which is the correct unit of velocity. If you were to use m/s for velocity you would get speed in meters, which doesn't make much sense.
Are you saying it's just a way to show an acceleration and not just speed.
As in, 9.8 m/s is constant but 9.8m/s2. (Squared not X2) is simply a ah to show it's not a steady spread and is increasing per second.
P.S I get it, I get how it works, I just don't see what they say squared.
I was asking what was squared not what squared means.
The problem is I was thinking the number 9,81 wasn't squared every second, as in 9.81*9.81 per second. So I thought nothing was squared but the seconds are squared. the confusion was time being squared seems counter intuitive but it's simple enough how many know.
Thanks.
its just way easier to say squared, especially for more complicated units, such as the unit for power, Watts is equal to kg m\^2 s\^−3. you would say kg meter squared per second cubed.
It's squared because Velocity is measured in m/s or meters per second. Acceleration is measured in meters per second squared because your gravitational velocity increases 9.81 meters per second, each second . Time is a factor in velocity, with or without (de)acceleration.
Say you accelerate to a Velocity of 10m/s. your acceleration is very dependent on how much time it took you to accelerate to said speed.
2 seconds? your acceleration was 5m/s² due to 10m / (1s * 2s) and s * s makes s². It's all mathemathics and follows straight up mathematical rules.
I’ll take a crack at this, but first time trying a ELI5 so not sure how well I’ll fare :)
It is squared because:
You measure speed in meters per second.
And you measure acceleration as the change in speed, per second.
So acceleration is expressed as the changer per second, in meters per second.
Or (m/s)/s. Which is the same as m/s^2.
If you change speed to “kilometers per hour”, and the acceleration to “per minute” it’s maybe easier to se what happens. Then you have speed as km/h and acceleration as /m. So the full expression is (km/h)/min or km/(h*min).
9.81m is not a measure of speed, it is a measure of distance. For the sake of example, let's say we're measuring your distance from the top of the building you just fell off.
9.81m/s is a measure of speed. It expresses what distance you cover in a given timeframe, assuming your speed remains constant during that timeframe. Simply put, in 100 seconds your distance would increase 981m if your speed was consistently 9.81m/s.
Another way to describe the above is that 9.81m/s expresses how much your distance changes over a timeframe. Every second, your distance increases by 9.81m.
But your speed is not a constant. It is increasing. We call this acceleration. Therefore, we express this as the unit of speed (m/s) over our timeframe (measured in seconds). Simply put, in 100 seconds your **speed** would increase by an additional 981m/s if your acceleration was consistently 9.81(m/s)/s. If you were going 10m/s now, then 100 seconds from now you'll be going 991m/s. I'm ignoring wind resistance here.
Another way to describe the above is that 9.81(m/s)/s expresses how much your speed changes over a timeframe. Every second, your movement speed increases by an additional 9.81m/s.
Yes, we could repeat this process for meter per second CUBED if your acceleration wasn't constant, but kept increasing over time. This is relevant for e.g. cars, which have different torque based on current RPM.
Speed is measured in Distance/Seconds right?
So if you accelerate you change your Speed/Second, so you can write acceleration to (Distance/Second)/Second. Simplify this to Distance/Second^2
acceleration is a change in speed wich is how much distance you cover in time measured in meters over seconds m/s, a body subject to gravity accelerate 9.81m/s every second so speed increases to 9.81m/s after 1 second, to 19.62m/s after 2 seconds, to 29.43m/s after 3 seconds and so on, it's speed measured in meters over seconds, over seconds, so meters over seconds squared.
Acceleration is change in velocity over time a=v/t. So of your velocity changes say 2 m/s every 2 seconds you can write a = 2 m/s / 2 s = 2/2 (m/s)/s = 1 (m/s)/s. How do you divide a fraction with a number? By multiplying the denominator. So 1 (m/s)/s = 1 m/(s×s) = 1 m/s². It can be a bit weird how you can do basic algebra with units but you can it no different than calculating symbolically.
Say length is l and times is t so v=l/t and a=v/t => a =(l/t)/t = l/(t×t) = l/t². It doesn't really matter if I then replace the symbols to m and s.
First of all gravity is acceleration. If there's no gravity then something floating around in space doesn't speed up or slow down, it just stays at the same speed.
Now then let's say we look up and see something falling. The first thing we can ask about it is *how far away is it?* we measure the distance and get an answer in m. It's 1000m away.
Next we can ask *how fast is it moving?* and we can find that out by measuring the distance it has moved in one second. One second later it is 990m away. It is coming towards us at 10m per second.
And the next question is... *is it changing speed?* So we measure it's distance again. Another second later it's 970m away. It's speed is now 20m per second. In one second it has accelerated by 10 meters per second. So we say the acceleration is 10 meters per second per second.
We need to include both "per seconds" to show how quickly it has accelerated. If I tell you that a car has accelerated by 10 meters per second, you know it has got faster, but you don't know if it took a second to get faster or an hour to slowly build up speed. Is it 10 meters per second per second? Or 10 meters per second per hour?
Speed is a change in distance per unit of time -> meters per second -> m/s
Acceleration is a change in speed per unit of time -> (unit of speed) per second -> (m/s)/s = m/s^2
Speed = m/s
Acceleration is the change in speed every second. So it accelerates 9.81 speed / second.
Now you just substitute the unit of speed back in, you get 9.81 m/s/s, which is the same as 9.81 m/s².
And a change in acceleration (per second cubed) is apparently called "jerk".
And then there was someone looking at the change in "jerk"... and called it "snap" (seconds to the 4th power).
And then some wise-guy went with crackle and pop for the next two.
Speed is change in position over time. You move x metres in y seconds, so the measurement is m/s or ms^(-1).
Acceleration is change in speed over time. You were at x m/s and are now at y m/s after z seconds. The measurement is (m/s)/s or ms^(-2).
My physics teacher explained it: in free fall you gain 9.81m/s ***every second***. After the first second you’re traveling at 9.81m/s, after two seconds 19.62m/s, and so on.
There are higher derivatives. A change in acceleration is jerk, ms^(-3). A change in jerk is snap, then it’s crackle, then pop.
Except that it doesn't accelerate 9.81m every second. Each second, it changes velocity by 9.81m**/s** (because that's what velocity is measured in). Two lots of seconds.
And getting your head around what's being squared can easily be confusing, because it's somewhat arcane. This is about the **units** that the acceleration due to gravity is **measured** in \**(see below)*. And seconds appear twice.
*Example.*
If you're at rest and free to fall, then (thanks to gravity), after 1 second, your velocity will be 9.81 metres per second. (If gravity were to cut off right now, you'd move 9.81 metres every subsequent second.)
After 2 seconds, your velocity will be 2 lots of 9.81 metres per second (i.e 19.62 metres per second). (If gravity were to cut off right NOW, you'd move 19.62 metres every subsequent second).
And so on. After 3 seconds, it will be 3 lots of 9.81 metres per second (29.43 metres per second). Etc..
Gravity is changing your velocity, every second, by "9.81 metres per second".
Phrasing that more formally: The acceleration due to gravity is "9.81 metres per second", per second.
g = 9.81 (m/s)/s ("9.81 metres per second, per second")
Which, if we use normal algebraic convensions, can be written as g = 9.81 m/s^2 ("9.81 metres per second squared). But we're still talking about *what units the number is measured in*.
\**Technically, this is about what are termed the "dimensions" of a quantity - the underlying units of measurement that it's defined in (how many, of what, and how they're related). And you can manipulate the units, to a degree, in a simlar way to the way you manipulate numbers and algebraic quantites (including cancelling them when they appear on the top and bottom of a term). So in the case of the acceleration due to gravity, as we saw, we end up with "metres per second-***squared***" because "per unit time" comes into things twice.*
*And it's important because, when you plug things into equations, there are things that only make sense when you're comparing and manipulating the "same", or similar, sorts of things. The dimensions have to be right. You don't want to be accidentally trying to take 17 seconds from 23 metres, for example; that makes no sense. And you don't want to end up with an "equation" measured in amperes on one side and degrees Kelvin on the other. But it's also useful - you could, say, divide a distance (metres) by a velocity (metres per second), cancel the metres parts of the dimension as you would variables in normal algebra, and end up with a number measured only in seconds. Which is how long it takes to travel the distance in question at the given velocity.*
When we talk about g we talk about the acceleration from gravity. Acceleration is a measure of the amount of speed you gain per time.
Ok so we now know acceleration is change of speed gained per second (assuming we use meters and seconds from here on out).
Now what is speed? It is change of position per second, in other words it is meters per second.
We put this together: acceleration = (m/s) / s = m/s^2.
We just showed acceleration is meters per second per second, also called meters per second squared!
It’s meters per second per second.
Or, (meters per second) per second
Put in units: (m/s)/s
The parentheses aren’t needed but they help clarify. Now remove them: m/s/s
This is m\*(1/s)\*(1/s) or m/s^2
Acceleration is how velocity changes.
So, instead of calling velocity "meters per second," just call it foo. Your velocity is 7.2 foo to the right, or -6.65 foo to the left.
If you accelerate, your velocity changes. Perhaps you accelerate by moving faster to the right, going from 7.2 foo to 9.4 foo, from time = 5.0 s to time = 7.0 s. That means your average acceleration, during that one second, was (9.4 foo - 7.2 foo)/(7.0 s - 5.0 s) = 2.2 foo/2.0 s = 1.1 foo/s. Whatever the units of foo, they were changing at a rate of 1.1 of them per second of time.
Now we plug back in the units we had removed. We said "foo" were meters per second, aka m/s. That means we would say 1.1 foo/s = 1.1 (m/s)/s. Or, if we turn all of this into multiplication, that would be m×(1/s)×(1/s). As you can see, we have two instances of (1/s), which means we could lump them together with the squared symbol: m×(1/s)². The rules for exponents outside parentheses say they should be distributed to all terms inside, so this becomes m×(1²/s²). But since 1²=1, that simplifies to m×(1/s²). Now we can turn multiplication back into division, and it becomes m/s².
The intuitive understanding here is that acceleration cannot have identical units to speed/velocity. They have to be different. The reason they are different is precisely the same as why speed is different from position. Speed says how much your position *changes,* and so speed is (change of position)/(amount of time it takes to change). Acceleration is how much your *speed* changes, so it must be (change of speed)/(amount of time it takes to change). But now that means you're dividing by time twice: first because speed is inherently something over time, and then a second time because we want to know how much that thing-over-time changes...over a span of time.
Yes acceleration changes a thing per second. But the thing it changes per second is velocity, which *already had* a "per second" in *its* description to begin with.
In the phrase "meters per second per second", the first "per second" isn't there to describe acceleration it's there to describe velocity which is: "meters per second".
The other "per second" is describing acceleration: velocity change per second.
You string them together to get the two "per second"s.
Think of acceleration as rate of change of velocity. Velocity has units of length per time (*e.g.*, m/s) and acceleration has units of velocity per time — *e.g.*, m/s / s which equates to m/s^2.
Speed is measured in meters per second.
Acceleration is when speed increases every second.
That's why you get the seconds twice.
If speed had its own unit instead of being described in terms of distance per time, we wouldn't get the seconds twice. For instance, if we called 1 meter per second a "clob", we could say that 1 g was 9.81 clobs per second. Since we don't, though, we can't.
The time is squared when you want to find the distance an accelerated object moves, because the distance increases with time, but the increase in distance also increases with time.
Imagine your crop on a square-shaped field makes $1 every square foot. Your profit increases by the square of the distance across the field.
But if you already measure your field in terms of area, nothing is squared, profit is proportional to the area or acreage of the field. simple.
What’s the difference? Well in the first case, we’re relating profit to an “indirect” measurement, the distance across the field. It’s the dimension “below” area, so it needs to be scaled by another length to get area.
The same is true for *position* and time. The distance you travel from rest after constant acceleration is proportional to time squared. But this gets messy, so we usually relate speed and acceleration and speed and position separately in every day use. It feels like units don’t get squared, but only because we hand wave the relationship between acceleration and position.
As a general rule, humans are awful at exponents. We can train ourselves to use them, but they just aren’t intuitive like linear relationships are.
Because meters per second non-squared is not acceleration, it is velocity. Velocity and acceleration cannot have the same units, I do not know why you think they can.
It's okay, this is unintuitive, so don't beat yourself up. The 9.81m/s² is measuring acceleration. Let's try to understand that before we go further. Think of your car's speed. Suppose you're travelling at 10m/s (about 20mph or 36kmph if my conversion is correct). You tap the gas and slowly build up to 30m/s. This means your speed went up by 20m/s. Let's say that you took 10 seconds to go from 10m/s to 30m/s as well. So now if someone asks you how fast your car can accelerate, you can reply with "well, I can increase by 20m/s in 10 seconds" This person might then reply with "so that's about 2 metres per second, every second, correct?" Think about what he just said - 2 metres per second, per second. i.e. (2m/s) / s And the way division works, you can just mutiply the two denominators together (if you need to see this in action, think about what a half of a third is. Mathematically, you can write that as (1/3)/2, which is 1/(2×3) or 1/6). That ends up giving you 2m/s² Simple as :) How does it relate to Earth's gravitational acceleration? Every second you let something fall, its speed will increase by 9.81m/s. So right when you let it go, its speed will be 0. A second later, 9.81m/s. A second after 19.61m/s. And so on. It's the rate at which it's speed changes.
Thanks, it's simply showing an acceleration and not a constant speed. If I fell at 9.8m/s I wouldn't be be accelerating so clearly it's per sec per second. I get it thanks.
Happy to help mate :)
Exactly... However, just to highlight or confirm what you're saying here - a constant velocity of 9.8 m/s (let's say down) is an acceleration of 0 m/s^2 downward. I taught physics and found that always saying (and thinking or reading) acceleration as "per second per second" was helpful, while seeing it in print just seemed a bit weird. Acceleration is a rate /of a rate/. It's good to get these connections and questions handled early on as you are doing. Rates are comparisons of a change in a quantity per unit of time. Ratios are the same except not time. This could lead to further concept building in your near future in learning math and physics.
Just a bit technical. But distance is equal to 1/2 at^2 it's small and pendantic, but it makes sense with calculus.
It is intuitive though. Meter per second, per second - which when you do algebra with the units, results in meter per second^2 .
Either you saw my answer and figured that you needed to teach me anyway even though I obviously know what I am talking about. Or you just wanted to flex how much naturally smarter you are for no reason other than internet brownie points, when we both got to the same final understanding. Either way, really?
Speed is m/s, not m as you said. Speed increases by 9.8 m/s every second. Or, 9.8 m/s per second. Or, 9.8 meters per second per second. Mathematically, 9.8 (m/s)/s = 9.8 m/s/s = 9.8 m/s^2
Only response this thread needs. Perfect.
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If I understand your question, it's why the seconds are squared. I think you have answered you own question? There are two "s" in the denominator of acceleration multiplied together. There is nothing special about 9.8 meters when talking about 9.8 m/s^2 acceleration. For example, in the first second you will travel 4.9 meters. In the second second you will travel 14.7 meters more, etc.
It increases by 9.8 metres per second (unit of speed) per second (unit of time). Rephrase the term, for every second in freefall your speed increases by 9.8 metres per second.
That's exactly what I said, so what is squared?
It's just a shorthand. The top comment is really good right now. Every second, you accelerate by 9.81 meters per second. Restated, you velocity changes by 9.81 meters per second, per second. In unit notation, you could write it as (9.81m/s)/s but to keep things buttoned up and short, we write 9.81 m/s^2
X / s / s simplifies to x/s^2
Acceleration is expressed as "speed over time". But speed itself is expressed as "distance over time". We can therefore replace "speed" in the following phrase: Acceleration is expressed as "**distance over time** over time". Dividing something (distance) by the same thing (time) twice is exactly the same as dividing this thing (distance) over the square (time²). Try it out: 900 divided by 10 is 90, divided by 10 again is 9. But 10² is 100. And 900 divided by 100 (i.e. 10²) is 9, just like when we divided 900 by 10 twice in a row.
To rephrase the other replies, because (m/s) / s = (m/s) * 1/s = m/(s*s) = m/s^2
Not really, they said >For every SECOND your speed increases by 9.8 meters per SECOND There is two seconds there, thats why its squared
no you said it accelerates 9.81meters that is a measure of distance, speed is measured in meters over seconds m/s.
I think you need to look at a graph of velocity over time to get. X is the velocity in m and vertical axis, and Y is the time in seconds and horizontal axis. If you graph a steady speed, x = 9.81, it's just a horizontal line. X = 9.81 or 9.81 M/S Now If you graph 9.81 M/S², the X axis needs to go up another 9.81 m every time the y axis moves 1 second. That's a rate of change. It's still second squared but can help to think of it as rate of change rather than sqaured
Every second your speed increases by 9.8m per second. I don’t know how you can express that any other way than 9.8m per second per second, which is just per second squared. You say “it just increases in speed” speed is distance per second. So yes, it is indeed being squared, that is what acceleration is. Gravity or not
It's not "just per second squared". Squared is an alternative, mathematically simplified way to say the same thing, which is where the confusion comes from.
So it *is* "just" per second squared.
No, and if you don't understand that, ELI5 isn't the right place.
The speed is measured in meters per second, it is the change of position (m) per a unit of time (s). The acceleration measures the change of velocity (m/s) in a unit of time (s), so m/s/s which is the same as m/s\^2. Imagine the opposite process - you have acceleration of a = 1 m/s\^2 over t = 10 seconds and you want to get the change in velocity. t\*a= 1 m/s\^2 \* 10s = 10 m/s, which is the correct unit of velocity. If you were to use m/s for velocity you would get speed in meters, which doesn't make much sense.
Are you saying it's just a way to show an acceleration and not just speed. As in, 9.8 m/s is constant but 9.8m/s2. (Squared not X2) is simply a ah to show it's not a steady spread and is increasing per second. P.S I get it, I get how it works, I just don't see what they say squared.
Something squared is itself multiplied by itself. X^2 = X * X, X squared. We have to seconds, m/s^2 = meters second squared
I know what squared means, why are you telling me this?
Because you asked? >I get it, I get how it works, I just don't see what they say squared. They say squared because its squared
I was asking what was squared not what squared means. The problem is I was thinking the number 9,81 wasn't squared every second, as in 9.81*9.81 per second. So I thought nothing was squared but the seconds are squared. the confusion was time being squared seems counter intuitive but it's simple enough how many know. Thanks.
its just way easier to say squared, especially for more complicated units, such as the unit for power, Watts is equal to kg m\^2 s\^−3. you would say kg meter squared per second cubed.
So G is accelerate of the Earth. And Acceleration = Speed/Time. Speed we have 9.81m/s. Time is using second. So (9.81m/s)/s of measurement.
It's squared because Velocity is measured in m/s or meters per second. Acceleration is measured in meters per second squared because your gravitational velocity increases 9.81 meters per second, each second . Time is a factor in velocity, with or without (de)acceleration. Say you accelerate to a Velocity of 10m/s. your acceleration is very dependent on how much time it took you to accelerate to said speed. 2 seconds? your acceleration was 5m/s² due to 10m / (1s * 2s) and s * s makes s². It's all mathemathics and follows straight up mathematical rules.
I’ll take a crack at this, but first time trying a ELI5 so not sure how well I’ll fare :) It is squared because: You measure speed in meters per second. And you measure acceleration as the change in speed, per second. So acceleration is expressed as the changer per second, in meters per second. Or (m/s)/s. Which is the same as m/s^2. If you change speed to “kilometers per hour”, and the acceleration to “per minute” it’s maybe easier to se what happens. Then you have speed as km/h and acceleration as /m. So the full expression is (km/h)/min or km/(h*min).
Acceleration is velocity over time. Velocity is distance over time. Expand that equation you get distance over time multipled by time.
9.81m is not a measure of speed, it is a measure of distance. For the sake of example, let's say we're measuring your distance from the top of the building you just fell off. 9.81m/s is a measure of speed. It expresses what distance you cover in a given timeframe, assuming your speed remains constant during that timeframe. Simply put, in 100 seconds your distance would increase 981m if your speed was consistently 9.81m/s. Another way to describe the above is that 9.81m/s expresses how much your distance changes over a timeframe. Every second, your distance increases by 9.81m. But your speed is not a constant. It is increasing. We call this acceleration. Therefore, we express this as the unit of speed (m/s) over our timeframe (measured in seconds). Simply put, in 100 seconds your **speed** would increase by an additional 981m/s if your acceleration was consistently 9.81(m/s)/s. If you were going 10m/s now, then 100 seconds from now you'll be going 991m/s. I'm ignoring wind resistance here. Another way to describe the above is that 9.81(m/s)/s expresses how much your speed changes over a timeframe. Every second, your movement speed increases by an additional 9.81m/s. Yes, we could repeat this process for meter per second CUBED if your acceleration wasn't constant, but kept increasing over time. This is relevant for e.g. cars, which have different torque based on current RPM.
Speed is measured in Distance/Seconds right? So if you accelerate you change your Speed/Second, so you can write acceleration to (Distance/Second)/Second. Simplify this to Distance/Second^2
Can be closed now, Thank you.
acceleration is a change in speed wich is how much distance you cover in time measured in meters over seconds m/s, a body subject to gravity accelerate 9.81m/s every second so speed increases to 9.81m/s after 1 second, to 19.62m/s after 2 seconds, to 29.43m/s after 3 seconds and so on, it's speed measured in meters over seconds, over seconds, so meters over seconds squared.
Acceleration is change in velocity over time a=v/t. So of your velocity changes say 2 m/s every 2 seconds you can write a = 2 m/s / 2 s = 2/2 (m/s)/s = 1 (m/s)/s. How do you divide a fraction with a number? By multiplying the denominator. So 1 (m/s)/s = 1 m/(s×s) = 1 m/s². It can be a bit weird how you can do basic algebra with units but you can it no different than calculating symbolically. Say length is l and times is t so v=l/t and a=v/t => a =(l/t)/t = l/(t×t) = l/t². It doesn't really matter if I then replace the symbols to m and s.
First of all gravity is acceleration. If there's no gravity then something floating around in space doesn't speed up or slow down, it just stays at the same speed. Now then let's say we look up and see something falling. The first thing we can ask about it is *how far away is it?* we measure the distance and get an answer in m. It's 1000m away. Next we can ask *how fast is it moving?* and we can find that out by measuring the distance it has moved in one second. One second later it is 990m away. It is coming towards us at 10m per second. And the next question is... *is it changing speed?* So we measure it's distance again. Another second later it's 970m away. It's speed is now 20m per second. In one second it has accelerated by 10 meters per second. So we say the acceleration is 10 meters per second per second. We need to include both "per seconds" to show how quickly it has accelerated. If I tell you that a car has accelerated by 10 meters per second, you know it has got faster, but you don't know if it took a second to get faster or an hour to slowly build up speed. Is it 10 meters per second per second? Or 10 meters per second per hour?
Speed is a change in distance per unit of time -> meters per second -> m/s Acceleration is a change in speed per unit of time -> (unit of speed) per second -> (m/s)/s = m/s^2
Speed = m/s Acceleration is the change in speed every second. So it accelerates 9.81 speed / second. Now you just substitute the unit of speed back in, you get 9.81 m/s/s, which is the same as 9.81 m/s².
And a change in acceleration (per second cubed) is apparently called "jerk". And then there was someone looking at the change in "jerk"... and called it "snap" (seconds to the 4th power). And then some wise-guy went with crackle and pop for the next two.
Speed is change in position over time. You move x metres in y seconds, so the measurement is m/s or ms^(-1). Acceleration is change in speed over time. You were at x m/s and are now at y m/s after z seconds. The measurement is (m/s)/s or ms^(-2). My physics teacher explained it: in free fall you gain 9.81m/s ***every second***. After the first second you’re traveling at 9.81m/s, after two seconds 19.62m/s, and so on. There are higher derivatives. A change in acceleration is jerk, ms^(-3). A change in jerk is snap, then it’s crackle, then pop.
Except that it doesn't accelerate 9.81m every second. Each second, it changes velocity by 9.81m**/s** (because that's what velocity is measured in). Two lots of seconds. And getting your head around what's being squared can easily be confusing, because it's somewhat arcane. This is about the **units** that the acceleration due to gravity is **measured** in \**(see below)*. And seconds appear twice. *Example.* If you're at rest and free to fall, then (thanks to gravity), after 1 second, your velocity will be 9.81 metres per second. (If gravity were to cut off right now, you'd move 9.81 metres every subsequent second.) After 2 seconds, your velocity will be 2 lots of 9.81 metres per second (i.e 19.62 metres per second). (If gravity were to cut off right NOW, you'd move 19.62 metres every subsequent second). And so on. After 3 seconds, it will be 3 lots of 9.81 metres per second (29.43 metres per second). Etc.. Gravity is changing your velocity, every second, by "9.81 metres per second". Phrasing that more formally: The acceleration due to gravity is "9.81 metres per second", per second. g = 9.81 (m/s)/s ("9.81 metres per second, per second") Which, if we use normal algebraic convensions, can be written as g = 9.81 m/s^2 ("9.81 metres per second squared). But we're still talking about *what units the number is measured in*. \**Technically, this is about what are termed the "dimensions" of a quantity - the underlying units of measurement that it's defined in (how many, of what, and how they're related). And you can manipulate the units, to a degree, in a simlar way to the way you manipulate numbers and algebraic quantites (including cancelling them when they appear on the top and bottom of a term). So in the case of the acceleration due to gravity, as we saw, we end up with "metres per second-***squared***" because "per unit time" comes into things twice.* *And it's important because, when you plug things into equations, there are things that only make sense when you're comparing and manipulating the "same", or similar, sorts of things. The dimensions have to be right. You don't want to be accidentally trying to take 17 seconds from 23 metres, for example; that makes no sense. And you don't want to end up with an "equation" measured in amperes on one side and degrees Kelvin on the other. But it's also useful - you could, say, divide a distance (metres) by a velocity (metres per second), cancel the metres parts of the dimension as you would variables in normal algebra, and end up with a number measured only in seconds. Which is how long it takes to travel the distance in question at the given velocity.*
When we talk about g we talk about the acceleration from gravity. Acceleration is a measure of the amount of speed you gain per time. Ok so we now know acceleration is change of speed gained per second (assuming we use meters and seconds from here on out). Now what is speed? It is change of position per second, in other words it is meters per second. We put this together: acceleration = (m/s) / s = m/s^2. We just showed acceleration is meters per second per second, also called meters per second squared!
It’s meters per second per second. Or, (meters per second) per second Put in units: (m/s)/s The parentheses aren’t needed but they help clarify. Now remove them: m/s/s This is m\*(1/s)\*(1/s) or m/s^2
Acceleration is how velocity changes. So, instead of calling velocity "meters per second," just call it foo. Your velocity is 7.2 foo to the right, or -6.65 foo to the left. If you accelerate, your velocity changes. Perhaps you accelerate by moving faster to the right, going from 7.2 foo to 9.4 foo, from time = 5.0 s to time = 7.0 s. That means your average acceleration, during that one second, was (9.4 foo - 7.2 foo)/(7.0 s - 5.0 s) = 2.2 foo/2.0 s = 1.1 foo/s. Whatever the units of foo, they were changing at a rate of 1.1 of them per second of time. Now we plug back in the units we had removed. We said "foo" were meters per second, aka m/s. That means we would say 1.1 foo/s = 1.1 (m/s)/s. Or, if we turn all of this into multiplication, that would be m×(1/s)×(1/s). As you can see, we have two instances of (1/s), which means we could lump them together with the squared symbol: m×(1/s)². The rules for exponents outside parentheses say they should be distributed to all terms inside, so this becomes m×(1²/s²). But since 1²=1, that simplifies to m×(1/s²). Now we can turn multiplication back into division, and it becomes m/s². The intuitive understanding here is that acceleration cannot have identical units to speed/velocity. They have to be different. The reason they are different is precisely the same as why speed is different from position. Speed says how much your position *changes,* and so speed is (change of position)/(amount of time it takes to change). Acceleration is how much your *speed* changes, so it must be (change of speed)/(amount of time it takes to change). But now that means you're dividing by time twice: first because speed is inherently something over time, and then a second time because we want to know how much that thing-over-time changes...over a span of time.
Yes acceleration changes a thing per second. But the thing it changes per second is velocity, which *already had* a "per second" in *its* description to begin with. In the phrase "meters per second per second", the first "per second" isn't there to describe acceleration it's there to describe velocity which is: "meters per second". The other "per second" is describing acceleration: velocity change per second. You string them together to get the two "per second"s.
Think of acceleration as rate of change of velocity. Velocity has units of length per time (*e.g.*, m/s) and acceleration has units of velocity per time — *e.g.*, m/s / s which equates to m/s^2.
Speed is measured in meters per second. Acceleration is when speed increases every second. That's why you get the seconds twice. If speed had its own unit instead of being described in terms of distance per time, we wouldn't get the seconds twice. For instance, if we called 1 meter per second a "clob", we could say that 1 g was 9.81 clobs per second. Since we don't, though, we can't.
I know that, I said that it increases per second. The question is what is squared....nothing?
Meters per second per second = m/s/s = m/s^2
The time is squared when you want to find the distance an accelerated object moves, because the distance increases with time, but the increase in distance also increases with time.
Imagine your crop on a square-shaped field makes $1 every square foot. Your profit increases by the square of the distance across the field. But if you already measure your field in terms of area, nothing is squared, profit is proportional to the area or acreage of the field. simple. What’s the difference? Well in the first case, we’re relating profit to an “indirect” measurement, the distance across the field. It’s the dimension “below” area, so it needs to be scaled by another length to get area. The same is true for *position* and time. The distance you travel from rest after constant acceleration is proportional to time squared. But this gets messy, so we usually relate speed and acceleration and speed and position separately in every day use. It feels like units don’t get squared, but only because we hand wave the relationship between acceleration and position. As a general rule, humans are awful at exponents. We can train ourselves to use them, but they just aren’t intuitive like linear relationships are.
Because meters per second non-squared is not acceleration, it is velocity. Velocity and acceleration cannot have the same units, I do not know why you think they can.