Reply to Brews ohare 

Brews, I am fully aware of the difference between kinematics and kinetics. This aticle doesn't need to involve that difference.

You quoted above an expression for acceleration. That expression is correct. I am not disagreeing with it. But it tells us absolutely nothing that would enable us to solve a motion problem.

To solve a problem in motion, we need an input force. If it only kinematics, we still need an input acceleration.

We always need some kinds of contraints or known accelerations before we can determine a trajectory.

The solution to your general acceleration equation above is "Anything".