Gist: Which direction counts as positive is chosen, not discovered. Fix it once at the start, and every sign that follows is relative to that choice — in the lecture’s words, “just the convention, my free choice”.
Why it matters: Velocity and acceleration only have signs because an axis was picked. Flip the axis and every sign flips with it, while the physics stays the same.
Detail: Lecture 2, p.1
Related: Average velocity, Instantaneous velocity, Physics