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This tag is for the classical concept of forces, i.e. the quantities causing an acceleration of a body. It expands to the strong/electroweak force only insofar as they act comparable to ‘classical’ forces. Use the [particle-physics] tag for decay channels due to forces and [newtonian-mechanics] or one of the other subtopics of [classical-mechanics] for the dynamics of classical systems.
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Is the average force calculated from $F(x)$ the same as that calculated from $F(t)$?
Your reasoning is valid with the important caveat that you yourself realized: this works if $x_1$ corresponds to $t_1$ and $x_2$ corresponds to $t_2$, and as long as the force over time and the force …