Car won't accelorate right away

The rpm go up-engine revs, but the speed doesn't increase
or seems rough as the rpms are going up?

I get the idea of a slipping tranny the way I read your post. Did you check the fluid level?

It may be slipping tranny or you may experience clutch slippage.
Clutch slippage is evident when the driver has the clutch engaged and the engine's speed increase but the vehicle's road speed does not.
To verify that:
Depress the clutch pedal, shift the transmission into higher gear and increase the engine's speed to approximately 2,000 rpm.
Slowly release the clutch pedal until the clutch engages. The engine should stall immediately. If the engine does not stall within a few seconds, The clutch is slipping.
*depress the clutch pedal to end the test quickly.

Hops! Is this a manual transmission? :)

This one didn't come with a munual transmission, but nice explaination none-the -less :)

At least this car must have a torque converter. :P
thank you paul for your input.I like construtive criticisms :)

changwang0, forget the manual transmission
If the engine's speed flares up when it accelerated in DRIVE and does not have normal acceleration, the clutches or bands in the transmission are slipping. This symptom is similar to the slipping of a clutch in manual transmission.