Depends on the carb, I suspect. The SU carbs for my MGA had dashpots to control how rapidly the venturi throat opened. It allowed it to close quite rapidly.
I don't know at all for that. The only bandsaws which I have experience with either have only step belt speed changes (the infamous "$200.00 horizontal/vertical bandsaw" sometimes sold for a lot less, and the three-wheel Emco one which I have), or the DoAll which we had at work with a variable speed pulley assembly, plus a gearbox to give a high range or a slow range. No dashpots involved in any of those as far as I know.
Mostly -- a dashpot is a cylinder with a very close fitting piston (often glass cylinder and graphite piston) with an adjustable needle valve to control how rapidly it could move. Could have an oil, or air as the medium. Then it is up to who put it in what as to whether it controls valves, limit switches, or whatever else. I could even imagine them being used in some record turntables to avoid rapidly dropping the stylus (needle) onto the record, possibly damaging both.) I've seen at least one model of turntable which has an arc support bar, and a lever which starts it lowering slowly, or lifts it to a safe height and keeps it there.
Enjoy, DoN.