Back end of car feels like it stutters when accelerating

I have a 2005 mustang gt (automatic). The problem is when ever i step on the gas to accelerate faster the back end feels like its stuttering to go or as if the tires are slipping, but im not pushing the pedal to the floor. One example is, i was on the highway going about 70mph and stepped on the gas a little to pass a car, rpms went to around 2500 and the back felt like the tires were slipping or they were stuttering to go. I checked the tires and they are good they arent low or have anything stuck on them. I really dont much about this car i just got it a couple months ago,I love the car but this issue is kind of scaring me if it is something serious. I dont know what it is any help would be great. Thanks!

Is your traction control on or off when you drive?

Transmission slipping?

Any lights come on when this happens?

Traction control is on is on, no lights come on, i also was thinking that the transmission might be slipping since sometimes when it shifts into another gear the car jerks forward and maksd a loud thunk sound

Could be the clutches in the rear end or the result of adding friction modifier when it's not needed. Either condition will result in grabby application of torque to one or both wheels due to the rear end clutches not holding higher power loads.

Not sure because I've never had them go out. However, they are a wear item and your car is getting along in years.