Physics equations are derived using calculus (which also involves some algebra). You can do physics and some physics simulations using only algebra (i.e. you are given what equations you need, and you "solve" for the variable you need). But this only works for the simplest, most basic physics simulations.

For everything else, you need calculus. You need to do numerical integration (the most popular methods for physics I've seen are semi-implicit Euler and RK4, sometimes Verlet too). Rotational physics use Jacobians. Collisions are often resolved using impulses. Basically, physics becomes a system of differential equations, and you need both algebra and calculus to solve it. This is one major reason people often use physics libraries instead of rolling their own physics engine; it's complicated and time consuming (and requires a good amount of background knowledge).

So if you're going to take a physics course, and you want to actually use physics, I'd take the calculus based course. They'll likely get into more of the "meat" of the physics, which is what you really need to do anything useful with physics. An algebra-based course will likely try to keep things too simple (where they'll just give you the equations instead of showing you how to derive them using calculus, and then you just solve for x).

That makes more sense but I'm not entirely sure what your two classes involves. It sounds like the algebra one might be an introduction to physics, whereas the calculus one is a more advanced dynamics class?

The most basic physics system in a game is very simple. You use forces to compute acceleration, add acceleration to velocity, then add velocity to position.

gameplay variables:
  gravity = Vec3D( 0, -9.8, 0 );
  thruster = Vec3D( 100, 0, 0 );
...
every frame:
  acceleration = gravity + thruster;
  velocity = velocity + acceleration * elapsedTime;
  position = position + velocity * elapsedTime;

However, that above bit of code actually represents an approximate solution to integrating the basic formula for constant acceleration:

s = ut+0.5at2

or

position = velocity * time + 0.5 * acceleration * time2

In that straightforward code, it doesn't look like you're using calculus; it just looks like some simple algebra. However, you've making use of Eulers method of numerical integration by advancing the simulation with small steps in time.

So, you can actually get a fair way without knowing a lot of calculus, and just relying on some tried and true integration techniques such as the above, without fully being able to derive them for yourself. The above few lines of code probably power hundreds of games