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Basic collisition resolution

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Can someone point me in the right direction in terms of basic 2D collision resolution? My simulation does not even involve rotation, so I'm currently looking for some "push physics" (a dynamic box collides with a static box and bounces off or comes to rest depending on the circumstances). What I'm thinking of doing is integrating the velocities/positions of the physics, then checking for collisions, and if there was a collision, move back the colliding bodies to their previous physics state and add some opposite velocities. However, I'm not sure what the proper collision response is in terms of velocity and position. (And, yes, I'm aware of existing solutions such as Box2D and Chipmunk, but the whole purpose of my project is to avoid pre-existing solutions - this isn't homework, though it is something I'm doing in school)

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