Sounds like tranny problem. Instead of mashing down the sccelerator... shift
your gear selector from D to 3... if you can accelerate fast with 3 then it
is not fuel problem.
When you accelerate moderately from stop to say 40 MPH... does it shift gear
so fast like from 1 to 4th and that it doesn't stay in 2 or 3rd for a while?
It is your tranny.