If you devote your time to it, that's definitely doable in one summer.
When I was making a
simple robot movement simulator, I often used the "Re/Im to Polar" and "Polar to Re/Im", for converting between Cartesian and polar coordinates. (They're found in the "complex" subpallette of Numeric)
If you're not already familiar with Sine, Cosine, and Tangent, you should become so.
As for actually creating the code, make sure to start with your definition. What do you want to accomplish? What are your inputs (controls)? What are your outputs (indicators)? You can create the front panel of your main VI first, and that will help define your code later.
(For example, you can have a VI that has the inputs of speed, direction, acceleration, rate of turn, and elapsed time, and the output of change in position. You know that every one of those inputs makes a difference in the value of the output. Now you just need to figure out WHAT the relationship is, and how you would describe that in a formula.)]
I have a brief overview of the process of software development here:
http://kamocat.com/programming/development.php
It's simple enough to not get lost in, but if you have any questions or need further detail, please ask.