Understanding Classical Mechanics: Acceleration

[Physicsphysics]

I'm reading once again through Landau-Lifchitz and I am stuck on the first page! I can't wrap my head around why we only need to define the coordinates and velocities to determine the acceleration? Surely if we only know those two in a single point in time, that's not enough to determine an acceleration? What am I missing here? Thanks!

 

[vanhees71]

From the equations of motion with given $q$ and $\dot{q}$ you get $\ddot{q}$. Of course you need the assumption that the (generalized) force depends only on $q$ and $\dot{q}$ as usual in classical mechanics.

 

[malawi_glenn]

Same question: https://www.physicsforums.com/threads/uniquely-defined-accelerations.1005819/

The phrasing "from experience" is what Vanhees is referring to I think, that the generelized force only depends on coordinates and velocities.