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Position and Displacement[edit]

The problem is not so much that "displacement" is a technical term but that it is actually incorrect to say that "velocity is the rate of change of displacement". Displacement is a change in position and so "change in displacement" divided by "change in time" becomes "change in the change of position" divided by time. This is a very common error that is advanced in many physics books as well as on many websites. It is something that can confuse students learning physics for the first time. For many professional physicists, the difference between a change in position and a change in displacement is something that they would consider trivial in that the context would often provide the necessary clarification. However the difference is important for proper concept formation at the foundational levels of learning in physics. I did try and correct this in August 2007 but with time the errors do seem to come creeping back. --Phillip (talk) 10:24, 23 December 2008 (UTC)

Completely wrong. Position is just some point in space, relative to some frame of reference. Displacement is a directional distance relative to some arbitrary fixed starting point. Speed is a scalar value. Velocity is a directional vector, and velocity is change of displacement over time as measured from some starting point. The average position is statistical point somewhere near the middle of all the positions. Average displacement is the directional distance of that middle point from the arbitrary starting point. BlueMist (talk) 23:06, 21 November 2014 (UTC)
For clarity, the position may be interpreted in one of two ways (unfortunately, these terms seem to acquire multiple meanings):
In this article, either interpretation works (despite any confusion of interpretation), because we are interested only in differences between positions, which are displacement vectors. I have chosen the term "position" over "displacement vector" because this most accurately reflects what is meant, and uses the least assumed mathematical structure on the space. To make the point more solidly, consider a manifold, which need not be flat. On this the concept of position is well-defined, as is the concept of velocity, but a displacement vector can only be defined on the tangent space (we can define infinitesimal displacements, but not larger displacements). This should be adequate to show that the second meaning of position above is the correct meaning to use in this article. —Quondum 02:44, 24 May 2015 (UTC)

One can precisely describe velocity in very few narrow, but useful terms. Velocity in Ballistics is not the same measurement implied by Medical Imaging. Ballistics describes Position and Displacement as Coil and Recoil. Position and Displacement of a moving ventricle/pump is measured as a specifically defined ratio between End Systolic Volume (ESV) and End Diastolic Volume (EDV) guided by selective phosphorylation of ATP. The ventricle, by virtue of a plurality of overlapping muscular strands adds the capability of Angular Velocity.--lbeben 02:40, 6 July 2014 (UTC)

Velocity in curved space[edit]

Since we dont have straight lines in curved space, how is velocity then defined?--Light current 01:20, 17 January 2006 (UTC)

Since velocity has both magnitude and direction, it is not necessary to have straight lines, although this means there is an acceleration. The velocity would still be defined as the derivative of the position of a particle with respect to time. Or, if you like, the speed of the particle in a direction tangential to the curve the particle is travelling on. I hope that helps! --Someones life 18:32, 4 February 2006 (UTC)

Question: If a particle has a defined position at every time, must it necessarily also have a defined velocity? Consider a particle moving along a line, so its position along the line at time t is x(t). Suppose we define x(t) as follows:

         { 1   if t > 0
 x(t) =  {
         { 0   if t <= 0

If I remember my calculus correctly, x'(0) is undefined, while x(t) = 0. Does it therefore follow that at time t=0, the particle has a position and is moving but has no velocity? Would it be physically possible (i.e. compatible with the laws of physics as we currently understand them) for a particle with that behaviour to actually exist? -- SJK

In classical (non-quantum) mechanics a particle with mass cannot make such an instantaneous jump in position. It implies infinite acceleration which implies infinite force. So this case is not physically possible in classical mechanics (assuming zero-mass particles are not physically possible). -- Eob
Eob: What about in quantum mechanics? IIRC, quantum mechanics predicts instantaneous jumps in position (consider e.g. the Bohr model of the atom). And it has a zero-mass particle, the photon... -- SJK
I was not sure about quantum mechanics which was why I explicitly restricted my comments to classical mechanics. But now that I consider it more I would hazard that the question that was posed is not meaningful in quantum mechanics because you can never know x(t) exactly. As for the The Bohr Model, it has been superceeded by a model of the atom surrounded by orbitals which are standing waves of the wave function, so I am not sure it is relevant. --Eob
the derivative of the step function x(t) you wrote above is the Dirac delta function. -- User:RAE
SJK: in Physics, if you can define exactly a position, you cannot define exactly a velocity. And vice versa. That's Heisenberg Uncertainty Principle:
A "velocity" is mathematical concept, not a physical concept. It's a distance divided by a time when the time is close to zero. It's a limit in mathematical terminology. "The laws of physics" and "mathematics" are not compatible. By the way, isn't that question some of your homework, mmh ?

Your function is not defined at zero, therefore x'(t) at t=0 is meaningless.

I am in browse mode tonight... but at some point a mention will have to made of tangent spaces and tie the discussion back to differential geometry.

Why is this article so bare?[edit]

I got a report to do, and I figured I'd get the info off of Wikipedia, and there is practically no history of velocity, like who thought of it and whatnot. Could someone fix it? —The preceding unsigned comment was added by (talk) 01:01, 14 February 2007 (UTC).


It's absolutely absurd that this article doesn't cover common units, abbreviations etc. What kind of reference work has equations without references!!! // FrankB 01:13, 14 August 2008 (UTC)

Simpler Equation?[edit]

I'm debating whether to put a simpler equation for calculating velocity as an addition to this article: d/t (distance divided by time). What do you think? "It's over 9000!" (talk) 06:10, 16 June 2009 (UTC)

What Happened!?[edit]

Who put, at the top of this page, a lowercase definition of velocity? And at least figure out the answer. Can someone please revert this change. Thank you.

Bab (talk) 01:53, 4 January 2009 (UTC)

May I add that the user is a IP address, and this vandlism has been done before. I repeat my revert cry.

Bab (talk) 01:59, 4 January 2009 (UTC)


dear wikipedia, i am in grammer school and i am asking you to pleese simplify some of the articals i do not understand them thank you, jzme

Velocity and speed[edit]

What exactly is their difference? Aren't they mostly the same? (talk) 20:52, 13 July 2010 (UTC)

Overly Complex Wording[edit]

I don't think this article has been written with a layman in mind. The concept of velocity and how it differs from speed (I would guess this is the primary reason someone would look at this article) is quite simple to explain, but the introduction doesn't do much in the way of explaining. There's a comment above from a school pupil stating that they didn't understand it and who could blame them? If my high school physics teacher had given me an explanation like that I'd have been completely lost. Blankfrackis (talk) 10:04, 1 August 2010 (UTC)

Speed and velocity[edit]

The article on speed is nice little article, with neat mathematical presentation. Still, it could be somewhat improved, particularly with respect to constant and average speed. Also, the use of the expression "distance travelled" (especially when without "travelled") may be misleading, the "length of the path travelled" would be better. But the main problem is that speed is explained (particularly in the lead) using a more complex notion of velocity.

This should be avoided in the lead, or the two articles should be merged. The velocity article is a mess anyway, and it should be written anew. The only issue is whether speed should be kept as a separate article. Any suggestions?--Ilevanat (talk) 00:42, 16 December 2011 (UTC)

Complete change to 'Equation of Motion' section[edit]

After looking through the section about 'Equation of Motion', I decided to rewrite it in order to include a more thorough definition of velocity and average velocity, as well as vector treatment of the constant acceleration equations and some more quantities that depend of velocity. I hope that you think it is slightly better now, but any help in making sure that it is both accurate and not too technical would be good. — Preceding unsigned comment added by DominicPrice (talkcontribs) 23:03, 5 May 2014 (UTC)

Add section on Special Relativity?[edit]

Anybody else think that this article could do with a section explaining the importance of the speed of light w.r.t velocity, and the effect of the concept of 'relative velocity'; I wouldn't know where to start or how much depth would be appropriate, but would be happy to help if someone could start this off?

Dominic (Imperial College) (talk) 12:19, 8 May 2014 (UTC)

"Instantaneous velocity"[edit]

Someone changed the redirect Instantaneous velocity to point to the section Velocity § Instantaneous velocity instead of simply to the article, which I reverted, because "instantaneous velocity" means the same as "velocity", and pointing the redirect to the section suggests otherwise. I made some edits in this article to make this clearer (along with unrelated edits). —Quondum 23:48, 23 May 2015 (UTC)

Who is redirecting Instantaneous velocity back to the top article?[edit]

More importantly, why are you saying "instantaneous velocity" is the same as "velocity" itself? It's not!

"Instantaneous velocity" is not the same as velocity itself, it's a TYPE of velocity! So is "average velocity"! They should both redirect to those particular sections of the article! 2601:E:2881:25B0:3D01:7E73:82A8:6018 (talk) 20:19, 28 May 2015 (UTC)

Could you please explain how velocity, when defined to be "the rate of change of its position with respect to a frame of reference", is distinct from "instantaneous velocity"? Your edit comment with this edit) (Not at any instant in time; that would be instantaneous velocity) suggest that you think that there is a distinction. —Quondum 23:53, 28 May 2015 (UTC)
To the IP - give explicit mathematical definitions of "velocity" and "instantaneous velocity" then (average velocity is obviously a seperate expression using the definitions of "velocity" and "average").
Fact is they are exactly the same: v(t) = d x(t)/dt where x(t) is the position vector (not displacement vector) of the particle. "Constant (or uniform) velocity" and "instantaneous velocity" are just terms to describe the state of the velocity of an object, they are not "types" of velocity. M∧Ŝc2ħεИτlk 11:37, 29 May 2015 (UTC)
To the IP: you will need to engage in this discussion if your opinion is to be considered before I again revert the redirect Instantaneous velocity so that it points to the top of this article (i.e. to Velocity rather than to its section Velocity#Instantaneous velocity). You appear to be editing from a dynamic IP address (limiting options for informing you), and so far you have not responded collaboratively. —Quondum 14:26, 30 May 2015 (UTC)