Is the position kinematic equation an approximation?

Question

Is the $Delta x=v_0t+frac{1}{2}at^2$ kinematic equation an approximation? I'm not asking with reference to relativity, but rather is it still an approximation within Newtonian Physics?
I remember deriving this equation from the definition of velocity, displacement, and acceleration. Therefore, it makes me think it is not an approximation. But, I also noticed it is just the first three terms of the Taylor series, which makes me think it is just an approximation (i.e. the Verlet method).
Also, what is the difference between this and the Verlet method?

John Darby · Accepted Answer

Your relationship is exact only for constant acceleration, $vec a$, based on solving $a = dv/dt$ for $v$, then solving $v = dx/dt$ for $x$.

maxbear123 · Answer

I just realized that the difference is the Verlet method is an approximation because it is applied to non-constant acceleration. I.e. the kinematic equation is not an approximation for constant accelerations.

Answered by maxbear123 on December 20, 2020

Is the position kinematic equation an approximation?

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