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newb
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Why is acceleration always squared?
Why Acceleration is Always Squared | Newbie Question Answered
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SUMMARY
The discussion clarifies why acceleration is expressed in units of meters per second squared (m/s²). Acceleration is defined as the rate of change of velocity, which is measured in meters per second (m/s). Since acceleration is the change in velocity per unit of time, it results in the unit being squared, as it involves time measured in seconds twice (per second, per second). Additionally, the conversation addresses the implications of applying force to an object in space, confirming that an object will continue to accelerate indefinitely if no opposing forces are present.
PREREQUISITES- Understanding of basic physics concepts such as force, mass, and acceleration.
- Familiarity with Newton's Second Law of Motion (F = ma).
- Knowledge of unit conversions, particularly in relation to velocity and acceleration.
- Basic mathematical skills for manipulating units and equations.
- Study Newton's Laws of Motion in detail to understand the relationship between force, mass, and acceleration.
- Learn about kinematics and the equations of motion for objects under constant acceleration.
- Explore unit analysis and dimensional analysis to reinforce understanding of physical quantities.
- Investigate real-world applications of acceleration in various fields such as engineering and astrophysics.
This discussion is beneficial for students new to physics, educators teaching foundational concepts, and anyone interested in understanding the principles of motion and forces in a scientific context.
Why is acceleration always squared?
- #2
Integral
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It's not.
v = at + v0
v = at + v0
- #3
jtbell
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F = ma
x = x_0 + v_0 t + \frac{1}{2} a t^2
x = x_0 + v_0 t + \frac{1}{2} a t^2
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- #4
Sojourner01
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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.
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.
- #5
LURCH
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Maybe Sojourner's response already made it clear enough, but:
Suppose I only told you I was traveling 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.
Suppose I only told you I was traveling 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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- #6
newb
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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.
(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.
- #7
Cyrus
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(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.
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.
- #8
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newb said:
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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- #9
BishopUser
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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)
- #10
newb
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Thanks for all the answers, I really appreciate it!