Acceleration

Is this the transmission that is kicking?
Or, is it strictly engine related?
Let me know and I am glad to help.

Does it downshift?
This is what should happen when you press down the pedal far enough. Did it downshift before this started?
Did it have any other problems shifting into gears very hard?
Dpes the transsmission, "Slip" as though the engine is revving faster than the transmission?
What happens when it, "catches up" with itself?

Is this from a dead stop?

To eliminate a few possibilities;
Check the trannsmission fluid level. The dipstick is on the driver side in the engine compartment. Warm the car up and put it into each gear, without moving, and then back into park while still running.
Pull the dipstick, (take note of the color and if the fluid looks dirty or smells burnt), Wipe it off and put it all the way back in. Take it out and check the level. You should see a low/cold level and a high/hot mark. The fluid should be between the 2 lines.
If not, top it off with the manufacturer Mitsubisdhi Giamond Transmission fluid ONLY. Do not over fill it either. If you think the transmission has had any other fluid other than the Mitsubishi Diamond, let me know. The Mitsu tranny is sensitive and will faill if other fluids are used.
Let me know how it goes.