There are many areas of game development, just as there are many areas of physics.
First, you will only need to know physics for games that require physics, obviously!If you're making an MMO, for example, you probably wont need physics.
But, as soon as there is any falling, velocities, acceleration and things like that involved, you'll need physics. Mostly, it's just movement stuff, m1v1 + m2v2 = m1v3 + m2v4, dS = V*dT, and your regular formulas you already know. I doubt that you will need anything more complicated from that, at least for now.
What is the problem, though, is applying physics. Collision detection isn't really an area of physics (or at least until you get to the subatomic level), but you still need it in your physics engine.