Why does my car hesitate for about 2 sec. then slowly accelerate when I push gas

What is your question?

When I let up on gas pedal & go to push it back down its has about a 2 second hesitation then very slow & smoothly increases acceleration until I let up on gas. Seem to always start up & take off ok after being turned off, but then within a couple/few minutes starts acting up again. What would cause that?