I'm not really sure how arbitrary acceleration is (like, if I can just choose an acceleration that makes the velocity vector erratically change directions while still keeping its length the same, or if such a thing would be called acceleration), so I've been kind of confused with this problem.
We've been learning about centripetal acceleration and circular motions in class, so that's probably related- but I don't have a clear idea how.
Can someone help me out?
No. The velocity has a constant length iff $$ 0 = \frac{d}{dt} \langle \vec v, \vec v \rangle = 2 \left \langle \frac{d\vec v}{dt}, \vec v \right\rangle $$hence iff the velocity is orthogonal to the acceleration. But the length of the acceleration is not constrained.