I was sort of thrown into teaching calculus based physics to a bunch of non-physics majors, who have taken one semester of calculus, and are poor with that material. It is only a 50 minute per week class. So I've been stuck in between teaching elements they'd receive in the calc sequence (integration by parts, $i$ and $j$ vector notation, dot product, partial derivatives, etc), and somewhat random integral or derivative versions of stuff they've seen in their normal physics class running in parallel. I also don't like the calc based text I'm using in parallel to their regular non-calc class text. Since it's a 50 minute per week, 1 credit hour class with low expectations, can anyone recommend me some "interesting" activities, or else point me to a nice standard problem set, to do in there?
I am going to assume that you are teaching a calculus "helper" versus the entire physics class. Your initial statements don't match that. But then all your content described is math, not physics. And also 50 minutes per week sounds rather light for a whole class. [If the converse is the case, I would spend your time on...physics.]
With that in mind, my advice is NOT to look for some interesting activities. Instead use this as an opportunity for you to learn about the math required in stereotypical physics 101 classes. And give the kids a brushup related to that. Look at the homework and see what are the key math steps in them. And give a little help on them. Don't teach the physics of it (no word problems, they get that in real class). But abstract it down just to the math itself.
I would try to parallel whatever is being done in physics class. If vectors are important this week, spend some time on vectors this week. If integrals are important a different week, spend time on that. Now, it may not match perfect match, and some remediation may be needed of issues in previous semester. But let that be a general guide.
In terms of format, I would try to do something interactive, using a handout each week. Some lecture and some practice, using the sheet.
I don't have any specific resources, but I suggest that you might find a little success by finding some physics applications where there really is a difference between the "algebra-based" and "calc-based" physics that use e.g. multivariate calc or integration by parts or something.
As an example, I think that there are some problems involving work (e.g. pumping water out of a conical tank?) that probably aren't exactly solvable without integrals, and which might require even trig substitution or worse. If you have access to a solution manual for the "real" calc-based physics course, you can just browse it for problems where those specific techniques come up, and then just do the problem up to the point where calculus comes in. Give them two minutes to talk to a neighbor to say "now what do I do", and assuming they have no idea, now you review the relevant calc technique.
This is probably not really going to help them internalize new calculus they need, but then again a 1-credit hour class probably is going to have pretty minimal expectations so at least it will connect a bit.