Hi last August I bought a 2002 Ford F 150 extended cab 4x4 only until the weather got really cold did I start noticing this kind of like almost vibration or like the rear end is slipping but it doesn't happen all the time it only happens when I take off but once I get driving then it goes away has anyone ever had this problem or does anyone have any ideas?

 

I'm not sure I understand you post but makes me think the emergency brake lining has come off the shoes and is binding up.
The parts have no place to fall out.
Good luck.

 

when your cruzing at 50 MPH, and push on the throttle does it do it again ? Maybe you have a misfire on one cylinder... COP problem ?

 

It only does the slippInge vibration when leaving from a dead stop once you get going items vibration is gone.

 

Better check 'dem' linings because that's the way they act.
Good luck.