It appears that velocity is a quantity of motion meaning that all objects can have assigned to them a particular velocity. Through the application of forces (ex: gravity, E&m) we measure changes in velocity, which is called acceleration but here is the crux:
Once the force ceases to be applied the body will stop accelerating.... Meaning that while forces can be applied there is no actual quantity of force
There exists a quantity called momentum (mv) such that a body of mass m with momentum Q will move indefinitely velocity Q/m unless acted on by a force (m*a)
There theoretically could be this thing called 2nd momentum (ma) such that a body of mass m with 2nd momentum Q would accelerate indefinitely unless acted upon by a 2nd order force (mass*jerk)
The reason the above ^ does not occur is because for it to occur would require a constantly increasing amount of energy... ie infinite energy.
But we don't actually mean energy, we mean the quantity 1/2 * mv^2 would grow arbitrarily large for this to occur...
In an abstract mathematical world where it is not 1/2 mv^2 that is conserved but rather the quantity 1/2 m*a^2 that is conserved objects could be in a state of uniform acceleration indefinitely and still satisfy conservation of 2nd order momentum...
But obviously our universe IS NOT that abstract mathematical world of the 2nd kind... It is of the first... Why? What dictated that momentum (mv) became the quantity of motion and not (ma) or for that matter (mass *jerk) or why not fractional derivatives of velocity?