Vibration on Acceleration and Coasting in High Gear

Kia Sportage 2001 4 cylinder
Little over 100,000 miles.
Manual Transmission

The Kia has recently developed a large vibration. It is most noticable when accelerating and when coasting in fifth gear. It seems to be originating from the rear of the vehicle. Cannot be 100% sure of that. Feels like it is causing a drain on the power. Anybody have any ideas?

More information.

It seems to be the most noticeable in third and fourth gear in a slow acceleration. Sounds somewhat like a car with loose items and a long continuous bass note from large speakers.

Easy things first: drive shaft U-joints. Mine had it on the front last fall...would show only in 4WD then , of course.

Thanks for the help. I am starting to believe it may be an engine problem. I had to sit in idle for awhile yesterday and I noticed that every minute or so the engine would start running rough. It is not continuous, or I couldn't feel it continuously. I thought this may be causing the vibration by uneven power at the wheels. Any ideas what would cause inconsistant engine trouble, that seems more noticeable when there is a strain on the engine?

..?? is the Check Engine Light ON? Misfires are a common plague on this car..maybe because of the heat containment around coils and wires...and codes come as P0301/2/3/4, depending on cylinder...

No the check engine light is not on. I changed the spark plugs and wires.

This problem did in fact end up being a bad U-Joint for anyone else that experiences a weird vibration. I must have read right over LMP's first great advice.