it all started with definition of velocity as: v = s / t (change of the position (displacemet) in certin time)
s represent displacement and
t change in time
then the acceleration as: a = v / t (change of the velocity in certin time) v represent change in velocity and t change in time
after some time "they" came to function (displacement) of s at some time t:
s(t) =s(0) + v*t + (1/2)*(at^2)
after that comes mathemacial manipulations....
somehow i belive it was well known before gallileo
albertlee about your question...niether there is such thing as regular velocity(v) in nature, its just how we call displacement in some time ...its just mathematics... but!! theres no such thing as mathematics its just human way of thinking .. it all started with counting sheeps and look where we have finished... im trying to say, dont try to picture everything because picturing is nothing but masking reality , hope you got it