On my 2000 XK8 54000mi. When cruising @ 30 or 40 mph. and I push down on the accelerator moderatly It dosen't seem to want to take it for a moment then it takes it. Could this be throttle cable adjustment? If so that seems fairly straight forward but you guys always have such good advice I would appreciate any comments or videos.

 

Probably not the cable, but the throttle body may need cleaning. Several threads here, just use the search.

 

The car also "learns" how you drive. If you drive normally (not aggressively) it assumes that is what you want and may not respond or kick down very quickly.

Put it in sport mode and see if the problem solves itself. If it does, then it has learned you are not a hot rod guy.

I would indeed check the cable and throttle body. The TB especially is prone to gunk collecting and keeping the fly from opening properly.