Donald G. Shead wrote:
Galileo discovered - with the crude methods available to him at the
time - that the rate of free fall starting from rest, was 16' per
second, and _changed_: Increasing at a _constant rate_ of 16' per
second each consecutive second that it continued: This constant rate
of change in the rate of free fall can be written in the language of
mathematics; as (16'/sec)/(1 second) = 16'/sec^2, and is a constant;
which is only one half [g/2] of Newton's acceleration of free fall [g
= (vt-vi)/t = 2s/t^2 = 32'/sec^2].

Now tell me; shock me; how can anybody refute Galileo's empirically
found Constant rate of free fall? Other than improving its accuracy
with today's methodology.

I think many of us here are rather more familiar than you with "the
language of mathematics". We know the equations to use when we wish to
calculate how long an object will take to fall a given distance, and we
know the constants to plug in so that our answers are in full agreement
with reality. Many of us have actually done the sodding experiment.

So, Shead, tell us how far an object falls (on Earth, neglecting air
resistance, initial velocity 0) in 5 seconds. You may assume a constant
value (of your choice!) for g.