Mathematics is the science of numbers and their operations.[1]

      In traditional mathematics, in calculus, one considers

a number - x -- whose value usually varies ( a variable)

a function - f(x) or y -- a really dependable rule that governs that number in the given situation

the derivative of that function - f'(x) or dy/dx - the function's rate of change

the second derivative of that function f''(x) or dy²/dx²
      -- the rate of change of the function's rate of change

the antiderivative of that function - ∫f(x)dx and often designated a F(X)
      -- the total result of the function from "start" to the given value of x.    
      Derivatives and antiderivatives/integrals are inverse functions and there are many of them.
      See stuff above for more on this.

 

      Mechanics is applied mathematics and deals with motion and forces producing motion. [2]

      In traditional mechanics, in kinematics (the "geometry of motion", of points, bodies/objects) [3], one considers

a time - t -- whose value usually changes positively (think goes to a longer period of time)

a position or distance or displacement - s(t)or d(t) from a "start"
      where the starting displacement is usually written as s(0) or s₀

      for example this use of a quadratic for model motion

the velocity - v(t) or s'(t) -- the derivative of displacement - the rate of change of the displacement, the "speed"

the acceleration - a(t) or v'(t) or s''(t) -- second derivative of that function
      -- the rate of change of the rate of change of displacement

the total displacement antiderivative of that function - ∫f(x)dx and often designated a F(X) -- the total result of the function from "start" to the given value of x
      This antiderivative is now named the absement.

 

      Negative Kinematics, Integral Kinematics [4], is all the integration functions of distance which have always existed but are now named and needed and used ]5].     Where only the traditional derivatives were named involving displacement (velocity, acceleration), now the antiderivatives are now also named ( absement, absity, ...), paralleling the reflection of unit name used in the metric system. SEE THE TABLE BELOW.

 

[0] https://www.gregorystrachta.com/94.html

[1] https://www.merriam-webster.com/dictionary/mathematics

[2] https://www.merriam-webster.com/dictionary/mechanics

[3] https://en.wikipedia.org/wiki/Kinematics

[4] http://wearcam.org/mannfit/IEEE_GEM2014_MannEtal_pages270-272.pdf

[5] http://wearcam.org/mannfit/

    In studying the fragment of history that led to the names for the nth derivatives, start with Roman numerals and Latin letters.

    In the mid1800s, chemists used small units (centimeters, grams, seconds) and engineers used large units (meter, kilogram, and second). When the Metric System was extend, it had toinclude all of these and more.[7]

    Use the prefix ab meaning “away.” "Other words with this prefix are: absent, abduct, and absolute. For example: Absent describes someone who is absent is “away” from a place.[8]

    As more units were needed, the naming became a bit quirky as with the naming of subatomic elementary particles of the Standard Model. The six "flavors" of quarks: up, down, strange, charm, bottom, and top. [9]

    Even Kellog's Rice Krispies Cereal [10] sounds, snap, crackle, and pop are found in the names of the nth-derivatives.

    The metric practice of using powers of ten and symmetry of names, large reflecting small for a specific power of 10, is used in naming the antiderivatives, the negative power nth derivatives.