In his reply to John Clement's well-stated points, John Denker writes
"There is every reason to believe they (acceleration and force) are
simultaneous, and no reason to believe otherwise. If anybody has
theoretical or experimental evidence to the contrary, please let us
know."
I think we should remember the distinction between the real world and
the models we construct to explain that world. Our model is based
around point particles and rigid bodies, neither of which exist in the
real world.
In the model we expect the unbalanced applied net force (John
Clement's push) and the acceleration of the point particle or the
rigid body to be simultaneous.
However in the real world, where elastic forces come into play as
existence of the unbalanced force is "communicated" to all parts of
the non-rigid body, simultaneity is not obvious.
But Leigh said all of this far better a few days ago:
"By hypothesis this equation applies strictly to a model. The model
closely resembles the phenomenon of a a physical body moving under the
influence of an applied force. It is in the details which distinguish
the model from the physical system that the causal relation between
force and acceleration is to be found. The gradual buildup of the
force over a very short time after its initial application and the
slight compression of the body over this same time interval will
corroborate the causal relation we naturally assign. In light of what
is really happening the metaphysical questions are readily seen to be
trivial."