my mac is running very slow ...will updating the mac will help?

Hello, it might, then updating might be a total disaster, I think we should investigate further. 🙂

See if the Disk is issuing any S.M.A.R.T errors in Disk Utility...

http://support.apple.com/kb/PH7029

Open Activity Monitor in Applications>Utilities, select All Processes & sort on CPU%, any indications there?

How much free RAM & free Disk space do you have also, click on the Memory & Disk Usage Tabs.

Open Console in Utilities & see if there are any clues or repeating messages when this happens.

In the Memory tab of Activity Monitor, are there a lot of Pageouts?

Also...

One way to test is to Safe Boot from the HD, (holding Shift key down at bootup), run Disk Utility in Applications>Utilities, then highlight your drive, click on Repair Permissions, Test for problem in Safe Mode...

PS. Safe boot may stay on the gray radian for a long time, let it go, it's trying to repair the Hard Drive

Reboot, test again.

If it only does it in Regular Boot, then it could be some hardware problem like Video card, (Quartz is turned off in Safe Mode), or Airport, or some USB or Firewire device, or 3rd party add-on, Check System Preferences>Accounts (Users & Groups in later OSX versions)>Login Items window to see if it or something relevant is listed. Or an errant process eating up RAM.

Check the System Preferences>Other Row, for 3rd party Pref Panes.

Also look in these if they exist, some are invisible...

/private/var/run/StartupItems

/Library/StartupItems

/System/Library/StartupItems

/System/Library/LaunchDaemons

/Library/LaunchDaemons