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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 at 12:14
  • $\begingroup$ @Conifold May I ask what the terms are in Russian? Regarding what makes sense, I disagree with your analysis; but this isn't relevant for this question, I believe (unless that really is the reason...) $\endgroup$ – Steeven Sep 12 at 12:51
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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 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 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 at 16:06
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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 at 1:00

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