Feel rumble when starting to move, then no more.

What is your question?

Upon acceleration from a stop, I feel a rumble and once moving it goes away. I feel the same in reverse. It is slowly becoming more obvious. It sometimes feels like the gas in the tank is slamming around during initial acceleration. There is no noise associated with it.

What makes this problem better or worse?

Makes no difference

How long has your 2008 Ford F-150 had this problem?

Several months