# Velocity is to speed as acceleration is to ________? [duplicate]

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?

• – AccidentalFourierTransform Dec 4 '19 at 21:07
• @AccidentalFourierTransform Definitely a duplicate of Is there a scalar acceleration?. – Graham Dec 5 '19 at 12:48
• "adjective: scalar : (of a quantity) having only magnitude, not direction" .... a scalar quantity. Alternate title for searchability: What is acceleration without a direction? – Mazura Dec 6 '19 at 3:04
• It is more accurate to construe scalars as having numerical values but no direction. A scalar can be negative, in which case its "magnitude" (which technically equals its absolute value) differs from its numerical value. (A vector, OTOH, is certainly well-characterised by its magnitude & direction.) – Ryan G Oct 10 at 16:39

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.

• 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 4 '19 at 21:05
• Sometimes the magnitude of the force vector is called "load", or "loading". – John Alexiou Dec 4 '19 at 23:13
• 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 5 '19 at 2:16
• @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 5 '19 at 5:50
• In natural language, velocity does not necessarily imply a vector (even after the distinction that Gibbs made). [Speed](www.merriam-webster.com/dictionary/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 5 '19 at 8:14

g-force is typically used to express the magnitude only, but the words are generally used interchangeably; laymen typically referring to the magnitude only.

• This is very specific to comparisons made with the force of gravity, but it does normally refer just to a scalar. – JPhi1618 Dec 4 '19 at 20:19

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.

• My actual use case was for function and variable names in python code. So I guess prefixing with ‘vector_...’ and ‘scalar_...’. – user209860 Dec 5 '19 at 13:18

Impulse required to start or stop something moving. Of course, there's mass involved, so you might want to take Impulse/mass

Speed-Up / Sped-Up