Why does my 04 Ford Mustang hesitates to accelerate?

My car stars up great and the transmission seems to work perfectly. However when I hit the gas, my cars hesitates to speed up. It vibrates to shift gears if I go easy on it. If i go a little hard it pulls back and then makes the shift. I have notice that when it is hesitating to accelerate I can help him by hitting the brake just for a sec and the hit the gas.

Note; it has an automatic transmission.
Sorry if i did not explain well.

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