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Vectors give both magnitude and direction, whereas scalars can be thought of as magnitude without direction. So, velocity is a vector since it is speed with direction. Similarly, what is the scalar analog of acceleration?

Velocity is to speed as acceleration is to ______. If there is nothing to fill that blank, is there a reason why velocity is so special?

Qmechanic
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5 Answers5

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In English, it seems that:

  • 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.
  • ...

Velocity/speed as well as position/length seem to be exceptions. The general trend is to not have different names for the scalar-forms of vectors.

In fact, I asked why this is the case on the History of Science and Math SE site a few months ago.

The answer told me that Gibbs and Wilson formally defined the difference between speed/velocity in technical English in 1901 in their book Vector Analysis:

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.

Since then, others continued this trend and it eventually got settled. Before then, the distinction was less clear.

In other languages, there is not necessarily such a distinction. It is consensus in English, Spanish, my mother-tongue Danish and others, but not in Russian, German etc.

Steeven
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    I think part of the reason is that in common parlance, 'speed' and 'velocity' only refer to the scalar. If I'm driving around a radius curve at a constant speed, my velocity is changing (in technical language) but in the vernacular, I'm driving at a constant velocity. – JimmyJames Dec 04 '19 at 21:05
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    Sometimes the magnitude of the force vector is called "load", or "loading". – John Alexiou Dec 04 '19 at 23:13
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    Also also, the change in acceleration over time (the third order derivative of position) is "Jerk." Snap (or Jounce, Crackle, and Pop are the fourth, fifth, and six respectively. – Draco18s no longer trusts SE Dec 05 '19 at 02:16
  • @JimmyJames Disagree completely. I have yet to hear anyone describe "driving at a constant velocity" outside of a technical context. Velocity IS a technical term. – Aron Dec 05 '19 at 04:44
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    @Aron I do hear velocity used as a scalar. For example, a "high velocity projectile." I think usually "velocity" means a vector quantity, but it doesn't seem to be universal. Its certainly better than other terms in that regard. – Cort Ammon Dec 05 '19 at 05:50
  • @CortAmmon-ReinstateMonica That example is fair. Also, I have heard of acceleration used in the scalar sense too, for example when talking about the capabilities of a performance vehicle. – Aron Dec 05 '19 at 05:56
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    In natural language, velocity does not necessarily imply a vector (even after the distinction that Gibbs made). Speed and velocity are actually still synonyms in more than one meaning. Only scientific use (mechanics branch of physics) makes this distinction, possibly because it was easier to say speed instead of magnitude of velocity all the time. – John Hamilton Dec 05 '19 at 08:14
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    In other words, the OP is looking at this the wrong way around. It's not that "velocity" is the exception in being a vector, but that "speed" is the exception being a magnitude and not a vector. – Graham Dec 05 '19 at 12:50
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    @Aron Lookup "high-velocity fan" for an example. Here's an example from an article titled "The Physics of speeding cars" where the terms are used more or less interchangeably: "If the car's initial speed was 70 kilometres/hour, the impact velocity would be 45 kilometres/hour, more than fast enough to kill." – JimmyJames Dec 05 '19 at 15:01
  • I'm surprised by your comment on Spanish, because I'm under the impression that velocidad is the primary word for speed and it's only for variety that people use synonyms (rapidez being the one that comes to mind). – Peter Taylor Dec 05 '19 at 15:01
  • @PeterTaylor Yes, there are various opinions on this, for instance on the Spanish SE site, where this question has been asked. I have asked a few Spanish-native engineering colleagues who confirmed that they basically don't have/use the distinction at all, not even technically - and that the term rapidez is equivalent to something like rapidness in English, which I wouldn't use in technical English anyways. – Steeven Dec 05 '19 at 17:54
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g-force is typically used to express the magnitude only, but the words are generally used interchangeably; laymen typically referring to the magnitude only.

Will Hatch
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    This is very specific to comparisons made with the force of gravity, but it does normally refer just to a scalar. – JPhi1618 Dec 04 '19 at 20:19
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If you need a word, coin it, define it in your writing and use it consistently. I would use hastening or quickening. For instance, an object going around in a circle at constant speed (thus angular velocity) isn't quickening, though it is constantly accelerating.

Kaz
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  • My actual use case was for function and variable names in python code. So I guess prefixing with ‘vector_...’ and ‘scalar_...’. –  Dec 05 '19 at 13:18
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Impulse required to start or stop something moving. Of course, there's mass involved, so you might want to take Impulse/mass

Yev
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Speed-Up / Sped-Up

From Google's definition:

noun an increase in speed, especially in a person's or machine's rate of working.

Some examples:

  1. I sped-up (accelerated) to catch my friends in front of me.
  2. Bobby will need to speed-up (accelerate) to overtake the race leader.
  3. The rocket fired its booster engines and sped-up (accelerated) to 10 km/s
Tim Andrews
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  • We do not say that since the magnitude of the train's velocity is 30m/s, the train speeds at 30m/s, so I don't think this is analogous to speed. – user253751 Dec 05 '19 at 11:39