No, that’s not apple meant to do.
iPad 2 is an old version and I think you used it for several years since you updated the software several times. Put the thought, that software update would cause old version slower, aside, have you tried to clean your iPad 2 storage space?
Software update would improve the performance of iPad. But the more important thing is that iPad should be cleaned since some unnecessary data or files, such as junk files, caches, history, corrupted files, etc., should lag the performance. Especially corrupted files would even cause cashes. So I do suggest you to clean your iPad regularly.
A simply way is to Reset your iPad with everything will be removed from your iPad. However, it is not suggested to do that because you need to configure your iPad from the beginning. Some important data or files will be removed as well. But if you want to try this way, you’d best back up the data to your iCloud or iTunes first. Besides, backing up the important files first is also important. Or it is hard or even impossible to find them back.
If you do not want to take this method, there are still some simple tips for your. They really work. You can refer here. I’m an apple user for 8 years, so I knew these tips work. Good luck!