Some questions have distinctly answerable parts (this one, for example).
If I know the answer to one part but not the other, is it acceptable to answer in part? I'm assuming that no better answers have appeared yet.
The difficulty probably comes for the asker when choosing the "correct" answer if/once someone else has answered the other half of the question. I have no solution to that problem. Maybe some questions should be split in two.
Nonetheless, an answer to only part of a question is worthwhile for several different reasons.
Yes, I definitely think that answering a part of a question is better than not answering at all.
The question shouldn't be asked this way.
That question is really two separate and distinct questions that should be asked separately.
I've left a comment to that effect.
Having thus rejected the premise of your question I could avoid answering it entirely, but I will say I agree with everyone else: Your answer doesn't need to be complete - we prefer that it be, but it's not a requirement. If you're providing correct information that addresses a substantial part of the question go ahead and answer.
Be aware that answers that do not fully address the question may not receive many upvotes, and may be downvoted for being incomplete - we have no control over how people elect to vote, so that's just a risk you have to take...
Your answer does not need to be complete, not at all. I'd say that anything that drives forward collective wisdom on the subject and isn't redundant is acceptable.
When I come across a question, which has multiple parts to it, and I know the answer to one or more parts but not all of them, I will usually start my answer with a brief summary of which parts the question consist of, and which of them will be addressed in my answer.
Then I will proceed to answer those parts, for which I do know the answer.
Whether a question with multiple parts to it should have been asked as a single question in the first place depends on how closely related those parts are. Whether it is best asked as one or two questions may not be clear to the person asking, sometimes you need to know both answers to see just how closely related the two questions are.
I suppose this is more about context than anything else. The 2 parts of the question are related to one another, and both questions are solvable with one answer (as I furnished the provided question with). It all depends on the asker, whether they deem them to be related enough to each other or not to ask them together. Naivity on the asker's part may lead them to think that both questions are related, when they aren't (though in this case, they are).
However, they also probably weren't expecting 1 answer to solve both of their questions simultaneously.
I also agree though, even if you don't know the entire answer, if you know something that may help, it's worth providing. As has been said previously, either a memory jogger, or something that could perhaps lead on automatically to a solution to problem #2 at the same time.