I just picked up a 05 f150 supercrew and ive noticed that it jerks a little when i give it gas from a dead stop. its not bad but i dont want it to lead to anything. it has 60k so i dont know if its just the things you live with in an older truck.

 

If it's only when the wheels are turned a little, probably rear axle clutch packs. If it has a two piece rear driveshaft, could be the support bearing. Some had trouble with slip yokes binding, where grease was added to the insides of the splines and that helped. Only things I can think of with your description.