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I'm looking at this graph from here:

enter image description here

The answer providing the above graph explains how kinetic friction is constant. However, the graph tells me that after static friction is overcome, there is a period of time where the kinetic friction is decreasing towards this constant value (the green part of the graph).

Given this, why is the force of kinetic friction still considered constant? It seems to be a function of velocity (approaching a certain asymptote as the velocity of an object approaches infinity).

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The coefficient of friction is not a perfect description of friction, but a simplified model that happens to be applicable over a wide range of materials and situations.

It's useful because the coefficient is nearly constant over such a large range. But the complexity of sticking and slipping is hidden by that assumption.

That said, I would interpret the graph and the other answer as saying the green section is a combination of a (constant) kinetic friction and static friction. That the material is beginning to slip, but still has periods when static friction is able to elevate the total force and only when you get to the blue section are you isolating the kinetic term.

However, you might prefer to model it differently, with a non-constant kinetic coefficient.

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