# Addes mass forces: can a force depend on acceleration?

I always interpreted "F=ma" as a cause-effect relationship, so I find rather uneasy to accept that the cause can instantaneously depend on the effect.

Is it fine to have a force which depends on an acceleration, in classical mechanics?

I came up with some possible solutions to this:

1. It's perfectly fine for F=m a to be an implicit equation with respect to a.
2. The time derivative of the velocity appears as the result of an approximation of a time-delay.
3. It arises due to assumptions made on the nature of the fluid (i.e. incompressible).
4. None of them
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–  Qmechanic Jun 28 at 20:06
There are two types of problems. a) Forward dynamics where $a=\frac{F}{m}$ or b) Inverse dynamics where $F = m a$.
The $F$ stands for net forces which includes applied forces, reaction forces, and friction forces. Applied forces are generally a function of time, position and velocity. Reaction forces directions are perpendicular to motions so to do no work and friction forces depend on other (interface) forces. So overall you do have cross-dependency on motion and forces in dynamics.