Physics Engine: Design Pattern

I'm writing a simple physics engine in JavaScript in order to make a few physics simulations and render them in a browser. I'm new to design patterns (so far I've only used the abstract factory design pattern for a Python project) so I wonder if you know a specific pattern that I can follow to fit my needs for the project (listed below, in order of importance):

1. Reusability of the code.
2. Good code organization.
3. Speed.