Constant acceleration equations are used to analyze projectile motion and help extract the value of unknown kinematic variables (velocity, distance, and time).
Gary Stephens
A good source of information can be found in the geometrical proofs given by Newton in his Principia.
For example his first demonstration "On first and last ratios . . " gives the distance (s) going as the duplicate ratio of the time (t^2). ---If I remember aright, Confer :
https://www.ncl.ac.uk/webtemplate/ask-assets/external/maths-resources/mechanics/kinematics/equations-of-motion.html
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