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However, the question (at least as I see it) is about
motivation. Why would one want to define v and a?
Why would one want to derive expressions that assume a constantacceleration?
It seems to me that one can either:that
(1) examine a case of free-fall empirically, which leads you to define
acceleration in order to describe the motion, and then use the finding
free-fall is characterized by constant acceleration to derive anexpression
for x; orforce
(2) examine what happens when a force is applied, which leads you to
Newton's 2nd law, and then use the assumption that gravity is the only
acting during free-fall to predict a constant acceleration and derive an
expression for x in order to test that prediction.