Integrating force with respect to acceleration

[Astro Boy 327]

So stupid question...but I integrated force with respect to acceleration and got 1/2(ma^2). Is there any "meaning" to this equation. I thought it was jerk but dimensional analysis doesn't give me units of m/s^3 but instead m^2/s^4 which makes no sense.

 

[andrewkirk]

I can see no meaning in it. I certainly would not expect it to be jerk. One can integrate almost any quantity with respect to any other quantity, and nearly all such arbitrarily chosen integrals are physically meaningless. One of the skills of a physicist is to identify which ones would be meaningful.