Bernard Cleyet wrote.....
Curious I thought there was only one -- from which all others (simple
ones not requiring Hamilton's principle, etc.) are derived.
I thought there were 2 (How can you derive anything from just 1?)
The definition of acceleration
a = (V - Vo)/t
and that distance traveled = average velocity × time
i.e. (x - xo) = {(V + Vo)/2}× t
noting average velocity is equal to the average of the initial and final
velocities if the acceleration is constant,