Hello, I have a 02 Ranger XLT. When I press the gas I get a shaky and slow acceleration until I hit 3k RPM then everything is normal while driving. Now if I slowly press the gas, everything is fine. Same thing happens when in park and the gas is pressed. Idle is fine, not rough or concerning at all.

The things my friend and I have tried:
Seafoam in gas
Replaced a suspicious spark plug
New fuel filter
Check for vacuum lost = None
Oil Change (because I needed one)
Checked throttle sensor

Any help is appreciated.

 

Welcome to the forum

For something like this I would spend the $20-$30 on an OBD2 blue tooth reader/scanner, you can see Live Data while engine loses power, and of course read codes
Get the $4-$8 extension cable with it
OBD2 is required BY LAW in all vehicles sold in the US or Canada since 1996, so not a Ford thing or even US car maker thing, it can be used on any vehicle if 1996 or newer, so a good investment if you plan on owning cars/trucks

You use these with FREE or $5 APPs on a smartphone, android or iOS
No I can't recommend a brand, check reviews and availability of APPs

As far as your symptom
When you step on the "air" pedal, no gas pedal on fuel injection engines, you increase the air flow into the intake, the computer is given a "heads up" for this by the Throttle Position Sensor(TPS), and then a second or two later by the increased air flow thru the MAF sensor, so instant response is why the TPS is there
Computer should respond by adding more fuel, Rich Mix, and decreasing Spark advance, Rich mix burns faster, so spark needs to be less advanced than when cruising along.
With a Scanner you can see all this happening or something not happening which should be.
Since your symptom effects RPMs from 1,000 to 2,900 I doubt it is TPS that would be short term and you would get a CEL(check engine light)

Since there is no code and no Fuel Pressure Sensor on these Rangers it could be your fuel pressure is marginal, 55PSI is specified, for 1998 to 2012 Rangers, if yours is lower then there could be enough of a drop when accelerating to cause the stumbling but enough pressure to maintain engine operation when cruising along.
You would see this as high fuel trims(STFT) on both banks when accelerating, +25% or more