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From: Tim Folkerts <tfolkert@FHSU.EDU>It *can* be the former, and it *is* the latter.
I don't view kinematics as derived from dynamics, or as a special case of
F=ma.
The kinematic equations are merely mathematical definitions. AfterWhat you say it true. However, students rarely recognize this no matter how hard we try to get the point across. They typically try to use these equations for cases where a is not constant.
DEFINING
v==dr/dt and a==dv/dt , you can use calculus to DERIVE x = 1/2at^2 +
v(0)t+ x(0), etc for constant acceleration, or DERIVE a = v^2/r for
circular motion. This has nothing to do with forces.
F = ma is a much deeper statement. You can determine mass; you canIt seems your words are true, but I don't understand the point.
determine acceleration; you can determine force. It turns out that,
EXPERIMENTALLY, F=ma. There is nothing that a priori requires this
particular relationship, it just happens that there is such a nice, simple
relationship in the universe. It is conceivable that an experiment might
disagree with F=ma and that it would have to be modified. But I don't see
how you could change a==dv/dt==d^2r/dt^2.