# Really newbie question

#### newb

Why is acceleration always squared?

Staff Emeritus
Gold Member
It's not.

v = at + v0

#### jtbell

Mentor
F = ma

$$x = x_0 + v_0 t + \frac{1}{2} a t^2$$

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#### Sojourner01

Are you asking why its units are ms^-2?

Because acceleration is rate of change of velocity. Rate of something is per second. Velocity is already metres per second - so acceleration is metres per second, per second.

#### LURCH

Maybe Sojourner's response already made it clear enough, but:

Suppose I only told you I was travelling at 3meters per second. You could know the total distance I'll travel in a given number of seconds by multiplying that number of seconds by 3 (6 meters in 2 seconds; in 5 seconds, 15 meters, and so on...). So rate of speed is a matter of multiplication, and the conjunction "per" actually means "multiplied by", or "times", and "meters per second" actually means "meters x seconds".

Well, I haven't given you enough information to tell what my rate of acceleration is, have I? But, if I tell you that I was standing still a second ago, and I'm moving at three meters per second (ms) now, and then a second later I tell you that I'm going six ms, you can determine a pattern. Although I've only reported my speed (in ms), you can see that every second, I'm going three meters per second faster than I was the second before, so I'm gaining three ms each second (or "per second"). So, you can tell how fast I'll be going a given number of seconds from now by multiplying that number (of seconds) times the 3 ms I'm gaining each second (after 1 second, I was going 3ms, after 3 seconds, 9ms; at 10 seconds, I'll be going 30ms and so forth...). Hence, three "meters per second", per second, or (since "per" means "times") "meters x seconds x seconds". And, since to multiply any number times itself is to square that number, "seconds x seconds" = "seconds2", so 3 mss = 3 ms2.

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#### newb

I'm new too physics and just learning about forces, energy,boyancy etc. but i'm having trouble understanding:

(1)why is acceleration m/s"squared"?
I don't understand why the "second" is "squared" why isn't the "meter" squared?

(2) If there's an object with a mass of 10kg in space and you apply 20N of force on that object, with no other influences that object will accelerate
a= 20N / 10kg = 10N/kg?

So the object would accelerate 10N/kg what does that even mean?!
And if that's suppose to mean 10m/s2 then does that mean the object will continue picking up speed forever since there's no force opposing it, or would it travel at some constant velocity?

I hope someone can understand what I'm trying to get out. Thanks.

#### Cyrus

(1) It is not meter per second "squared"

A second squared is meaningless. It is meter per second, per second, i.e. the time rate of change of velocity.

(2) Yes.

What is a Newton?

$$\frac {kg \cdot m}{s^2}$$

Yes, it will accelerate forever.

#### ZapperZ

Staff Emeritus
2018 Award
newb said:
I'm new too physics and just learning about forces, energy,boyancy etc. but i'm having trouble understanding:

(1)why is acceleration m/s"squared"?
I don't understand why the "second" is "squared" why isn't the "meter" squared?
You have asked this question before!

Several people have responded. What did you not understand out of those responses?

I'm going to merge that thread into this one, and then move it to the Homework forum where it belongs. Please post this type of question in that forum from now on.

Zz.

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#### BishopUser

It might be easier to think of it in a different velocity unit. Think of the acceleration in miles per hour per second. If your car accelerated at 10 miles per hour every second, then your needle on the speedometer would move up 10 miles per hour every second. Now if your speedometer was in units of meters per second (instead of miles per hour) it would be the same thing. If your car accelerated at 10 meters per second per second, then the needle would just move up 10 meters per second on the dial every second. Instead of saying "meters per second per second" we generally say "meters per second squared" (m/s^2 instead of m/s/s)

#### newb

Thanks for all the answers, I really appreciate it!

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