Sliding friction, position/velocity as a function of time?

AI Thread Summary
Calculating the position and velocity of a particle with non-zero velocity and acceleration, while accounting for sliding friction, is indeed possible. The friction force, which opposes movement, can complicate the equations of motion but can be integrated into a continuous model. The challenge lies in defining the function f(dt) that represents the effects of friction over time, as it may vary based on the particle's changing velocity and direction. Kinetic friction is inherently piecewise due to its dependence on the direction of movement and the forces acting on the particle. A continuous physics simulator can incorporate these dynamics by carefully modeling the frictional force in relation to the applied forces.
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If this question is completely stupid, forgive me, I'm a few years out of university and math and physics are quickly leaving my brain... :)

Say a particle has a non zero velocity in one direction and a non zero acceleration in the opposite direction. If you also account for some sliding friction force opposing this movement, is it still possible to calculate its position and velocity as functions of time?

I've been googling around for a while and can't seem to come up with what I want. I'm trying to write a little (extremely simplified) continuous physics simulator, and after some timestep dt I need to be able to say "new_x_position = velocity * dt + f(dt)" where f is some mystery function- right now the only things I can come up with are piecewise functions.

edit: I should clarify- the source of my confusion is that sliding friction can never exceed whatever applied force is causing the particle's acceleration, and must always oppose movement, even if the particle's direction changes during that timestep
 
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I guess this question could be summarised as, "Is kinetic friction inherently piecewise?"
 

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