Velocity is to speed as acceleration is to ________? 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?
 A: g-force is typically used to express the magnitude only, but the words are generally used interchangeably; laymen typically referring to the magnitude only.
A: 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. 
A: 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.
A: Impulse required to start or stop something moving.  Of course, there's mass involved, so you might want to take Impulse/mass
A: 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:


*

*I sped-up (accelerated) to catch my friends in front of me.

*Bobby will need to speed-up (accelerate) to overtake the race leader.

*The rocket fired its booster engines and sped-up (accelerated) to 10 km/s

