SLOW system due to Yosemite

Question

My Mac is from 2011, so I know it's 3.5 years old. However, it was running pretty good overall until I downloaded Yosemite. Now it is horrible. The start up time is ridiculously slow; my Safari screen freezes a lot and will just give me the spinning circle until I let it stop; and I am told every time I start up my computer that it needs to update. I just don't get it. I was told by an Apple store employee that even though my Mac is 3.5 years old, it should handle Yosemite perfectly fine. Has anyone else been having trouble with Yosemite? If yes, what have you done about it? The closest Apply store to me is 4-6 hours away, depending on which I would choose to go to. I can't justify driving that long just to get my computer checked.

Answer 1

When you see a beachball cursor or the slowness is especially bad, note the exact time: hour, minute, second.  
These instructions must be carried out as an administrator. If you have only one user account, you are the administrator.
Launch the Console application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad and start typing the name.
The title of the Console window should be All Messages. If it isn't, select
          SYSTEM LOG QUERIES ▹ All Messages
from the log list on the left. If you don't see that list, select
          View ▹ Show Log List
from the menu bar at the top of the screen.
Each message in the log begins with the date and time when it was entered. Scroll back to the time you noted above.
Select the messages entered from then until the end of the episode, or until they start to repeat, whichever comes first.
Copy the messages to the Clipboard by pressing the key combination command-C. Paste into a reply to this message by pressing command-V.
The log contains a vast amount of information, almost all of it useless for solving any particular problem. When posting a log extract, be selective. A few dozen lines are almost always more than enough.
Please don't indiscriminately dump thousands of lines from the log into this discussion.
Please don't post screenshots of log messages—post the text.
Some private information, such as your name, may appear in the log. Anonymize before posting.