It may be that you need to do a restart or a reset of the iPad2 after closing all the apps. To do all that:
Fully Close an App: Double tap the Home button (or do a 4-finger swipe up) to reveal a row of icons in the multi-tasking bar. Press and hold an icon until they all start to wiggle and you see a red circle with a minus sign ("-") in the top left. Press the minus sign to fully close the app. Don't worry, it won't remove the app from your iPad, just from the iPad's resident memory.
Then...
Restart: Hold down the power button until the power off slider appears. Slide it off. When the iPad finishes shutting down, hold down the power button again until the Apple logo appears.
See if that helped fix your slowness problem. If no, then do this:
Reset: Hold both the power and home buttons until the screen goes dark and the Apple logo then appears (the slide to unlock screen may or may not appear). Once the logo appears, release the buttons. After a time, your homescreen will appear. Please note that it may take some time for the Apple logo to appear or for your homescreen to appear (or both). This is normal. Eventually, the homescreen will appear.
As much as Apple likes to tell us different (or downplay it), the iPad is just a computer and so sometimes needs a swift kick in the software. So, see if this helps.
Good luck and do let us know how you get on.
Marilyn