# Why is there no such thing as a body in a state of acceleration?

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?

• Is this outside the realm of current research to determine? May 4 '13 at 3:39
• If you are familiar with Lagrangian mechanics, this question is actually equivalent to this one. That said, I'm disinclined to call it a duplicate, since they approach the issue from different directions. Also, it's not clear you'll get entirely satisfactory answers however this is asked.
– user10851
May 5 '13 at 20:52
• Thank you! This appears to be similar, it appears my actual physics knowledge versus what I want to know have a big disparity... Though I think this is a good step to fixing it May 5 '13 at 22:54
• I didn't realize this had been closed. Would someone enlighten me as to why a deep question about fundamental physical laws is "not constructive"? Perhaps it is a duplicate (see my above comment, and note that the answer there is not complete and seems to only apply to specific cases), but why is this perceived as argumentative?
– user10851
Jul 20 '13 at 6:28