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  • Position is a vector. Distance/length is a name of its magnitude.
  • Velocity is a vector. Speed is a name of its magnitude.
  • Acceleration is a name of a vector and its magnitude.
  • Force is a name of a vector and its magnitude.
  • Momentum is a name of a vector and its magnitude.
  • ...

Of all the vastly many types of vector quantities we traditionally have defined in physics (and other technical sciences), two leap out at us as oddly different, regarding their terminology: Position and velocity.

These two vectors have scalar magnitudes that are named differently than themselves. For all other vectors, the naming convention is to use the same term for both the vector itself as well as for its scalar magnitude. If we are talking about the vector or the scalar then depends on context - at least we don't have to memorise two terms for each defined vector quantity.

I am aware of the use in the English language. These many different words exist in English, sure, such as distance, length, displacement in relation to position, and such as speed in relation to velocity. But just because many words exist in the shared language, this doesn't have to require scientists to include all those words into accurate definitions in physics.

Are there any historical reasons for why only these two vector quantities have differently named scalar magnitudes, a practice which breaks the otherwise consistent terminology pattern, and a practice that confuses and complicates the introductory teaching of physics (these two quantites are after all the very first ones you learn about in your high-school and/or university science class).

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    $\begingroup$ This separation is not even universally followed, and in some languages (like Russian) non-existent. But it makes sense to emphasize the difference to beginners with different names, so later they are less likely to confuse vectors with their magnitudes (which they still do). And because they are the simplest (and the oldest), with the most colloquial uses and connotations, different names were more readily available for the task. $\endgroup$
    – Conifold
    Sep 12, 2019 at 12:14
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    $\begingroup$ Both speed and velocity are скорость in Russian. Also, distance or length are not the magnitude of the position vector even in English (it does not really have any physical meaning since depends on the choice of the origin). The reason is pedagogical rather than historical (unless you mean history of textbooks), it is also reflected in elementary texts boldfacing vector letters, or putting little arrows over them. They'd probably use a universal suffix construction for magnitude if there was one, instead of having to write "magnitude of..." to disambiguate, e.g. velocitude, forcitude, etc. $\endgroup$
    – Conifold
    Sep 12, 2019 at 19:40
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    $\begingroup$ The Russians are not alone... Germans use 'Geschwindigkeit' only. The French employ 'vitesse', and the Spanish 'velocidad'... $\endgroup$
    – xxavier
    Sep 15, 2019 at 9:23
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    $\begingroup$ I first learned position, velocity, acceleration in 1D linear motion. They were called “signed magnitudes,” not “vectors,” and were treated as real numbers, like distance and speed. Speed helped distinguish negative acceleration and the common notion of deceleration. Years later in physics vectors were introduced, and in higher physics the term “speed” seemed to drop out in favor of “velocity.“ Distance which corresponds to change in position has its own value in, say, distance traveled (arc length) which does not correspond to a vector. The parallelism being suggested is perhaps not absolute. $\endgroup$
    – Michael E2
    Sep 15, 2019 at 16:06
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    $\begingroup$ @Steeven You'll find 'rapidez' only in those physics books in Spanish that are translations of books written in English. The translator has resorted to the very artificial and unusual (in physics...) 'rapidez' in order to have two words and thus cope with 'speed' and 'velocity'... $\endgroup$
    – xxavier
    Sep 24, 2019 at 11:51

2 Answers 2

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Gibbs, the father of vector analysis in physics, or his student Edwin Bidwell Wilson, seems to have established the tradition of using the word speed for the scalar, and the word velocity for the vector. It seems to me that using these two different names was meant to be helpful when introducing vectors, rather than to confuse and complicate.

Gibbs's lecture notes on vector analysis and its use in physics circulated in a small circle since 1881. Wilson was asked to expand on these notes and write a textbook that would be more suitable as a first introduction to the subject. His book Vector Analysis (1901), had a huge influence, and it helped to standardize the notation and vocabulary. In the book, Wilson recommended using the words speed and velocity as follows: Velocity is a vector quantity. Its direction is the direction of the tangent of the curve described by the particle. The term speed is used frequently to denote merely the scalar value of the velocity. This convention will be followed here.

That recommendation was repeated by a popular physics textbook that was published a few years later: A Textbook on Physics by Duff (1909): For clearness such a phrase as 'twenty miles an hour' may be called the statement of a speed, which means the mere magnitude of a velocity without reference to the direction.

Before Gibbs the distinction between the words speed and velocity was less clear. For example, Maxwell discussed speed, velocity, vectors and scalars in his book Matter and Motion (1877). He said: The rate or speed of the motion is called the velocity of the particle, and its magnitude is expressed by saying that it is such a distance in such a time, as, for instance, ten miles an hour, or one metre per second.

(copied from a post by me in Physics Forums)

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  • $\begingroup$ You probably mean "Gibbs and Heaviside, the fathers of vector analysis in physics". $\endgroup$
    – John B
    Dec 5, 2019 at 1:00
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Having read @jkien's answer I have done done some research on the first use of the terms velocity and speed as we define them nowadays.

@jkien writes

Gibbs's lecture notes on vector analysis and its use in physics circulated in a small circle since 1881.

A copy of these notes by Gibbs, Elements of Vector Analysis arranged for the use of students of Physics dated 1884 has no mention of the word speed.

I then came across a copy of An Elementary Treatise on Kinematics and Dynamics by MccGregor published in 1887 which states in the Preface,

enter image description here

Now Tait wrote with Steele a textbook, A treatise on the Dynamics of Particles, which was published in many editions.

Comparing the Fourth Edition paragraph 8 published in 1878,

enter image description here

with the Fifth Edition paragraph 8 published in 1882,

enter image description here

one can see that Tait and Steele adopted the modern definitions of speed and velocity.

It might well be that around 1880 there were discussions amongst many English speaking scientists about the use of words speed and velocity and then a consensus was arrived at.

I am not certain as to which publication of Tait and Steele's MacGregor was referring to but it looks as though that somewhere between 1882 and 1884 formal definitions of speed and velocity were adopted.

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  • $\begingroup$ Many of the variant terminologies are a function of academic discipline and, in some cases, industry, e.g., physics, mathematics, statistics, engineering, and so on. Here's a recent paper further elaborating on this Eager et al., Beyond velocity and acceleration: jerk, snap and higher derivatives, 2016, Eur. J. Phys. 37, iopscience.iop.org/article/10.1088/0143-0807/37/6/065008/pdf $\endgroup$
    – DJohnson
    Jun 12, 2023 at 11:52
  • $\begingroup$ @Farcher - Great find that Tait introduced the distinction between velocity and speed. The 1883 version of the Encyclopedia Brittanica (link) may have helped to gain exposure. In this encyclopedia, Tait wrote an extensive article on Mechanics, in which he makes the distinction: 'velocity involves the ideas of speed and of direction of motion conjointly. It is, in fact, in the language of quaternions, a "vector," of $\endgroup$
    – jkien
    Jun 19, 2023 at 18:34
  • $\begingroup$ ... which the speed is the "tensor" or length, and of which the "versor" assigns the direction.' A book on Physical Arithmetic, by Macfarlane in 1885, says the 'distinction is due to Tait (Mechanics, Ency Brit, vol XV, p 688)', so MacFarlane refers to the encyclopedia instead of Tait and Steele's book. (link) $\endgroup$
    – jkien
    Jun 19, 2023 at 18:35
  • $\begingroup$ @jkien Many thanks for taking the trouble to dig deeper and find what I believe to be the definitive document which lead to the current definitions of speed and velocity. $\endgroup$
    – Farcher
    Jun 19, 2023 at 21:48

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