I thought I should include some more information.
I typed "glxinfo | grep render" in terminal to find the video driver installed
on my system and I got the following results:
"direct rendering: YesOpenGL renderer string: Mesa DRI R300 (RV380 5460)
20090101 x86/MMX/SSE2 TCL DRI2"
From the above information it does not seem to me that I have got the right
driver installed? Any suggestions?
I also tried to go to "Sytem > Administration > Hardware drivers", no
proprietary driver appear in the list.
The more i read on forums and investigate this problem, the more I become sure
that I am using a wrong graphics driver? I know that some people would say that
ubuntu needs a big resource power house, but, I still think that my laptop has
enough specs to deal with ubuntu.
Apologies for the long email.

Ubuntu is not the problem, Flash is the problem. (Or perhaps "rendering in a
browser" is the problem.)

There are add-ons to Firefox which let you download Flash videos to your
computer. You could always download the videos, then play them in VLC.

You are right I can do that. But, that's a bit tedious.
The only thing I cant get my head around is what is the cause of this problem. I
dont think now that Flash is the problem because I played videos with html5
format and still similar results.
I guess its my ati video card which is causing a problem. May be someone with a
more experience head can clarify this.

Also, if you need speed and don't need the add-ons do away with them or even
try a faster browser, such as Chromium, reKonq, Midori or Dooble. Firefox is
slower to begin with and when you add the Add-ons it is a lot slower.

I am using Chromium and I have got no extensions installed. I also tried opera
but no luck.
I came across couple of solutions. I was wondering if any one can help me on
this further.
1) One of the option was to go to "gstreamer properties" and the video output to
"No Xv". Can you please explain what this means?
2) The second solution was to modify "xorg.conf" (which does not exist in
10.04). In xorg.conf, edit the Device section and set the "AccelMethod to EXA.
Section "Device"
Identifier "ATI Radeon"
Driver "ati"
Option "AccelMethod" "EXA"
Option "MigrationHeuristic" "greedy"
Option "AccelDFS" "true"
Option "EnablePageFlip" "true"
Option "EnableDepthMoves" "true"
EndSection