How to treat noise (in the acceleration) in a Kalman filter when tracking position?
Uh, this is the whole point of a Kálmán filter.  It has a stochastic measurement model (noisy measurements) and a stochastic process state update model and uses the measurements for estimating the current state of the stochastic process.

If the process were deterministic, you would approach perfect information over time.

So you just plug the variation of your acceleration into the covariance matrix for the state update.

The exact way to do that depends on the conventions your course material employs (lots to choose from).