Why would my car accelerate on its own sometimes

have the fault codes read
check the accelerator position sensor or throttle body motor / sensor for problems

The Car comes to an stall when accelerating,pressing the gas pedal ...

https://answers.yahoo.com/question/index?qid...
Feb 7, 2007 - Sometimes when I press the gas pedal seems like nothing happens car doesn't accelerate at all only it loses the power and finally comes to a Stop, and sometimes it recovers (shakily) and keeps on truckin'. ... Does the engine shake andstall when you put the transmission into ... car stalls if gas pedal not pressed.?
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More results from answers.yahoo.com

Sounds like your spark plugs need replaced. ( long shot answer)

When was the last service done?

Sounds are kind of hard to describe. Bad exhaust noise can be noticed more when the exhaust is rushed in acceleration. Valve rattle can be created on acceleration as well as "spark knock".

Sometimes an air induction leak can roar when the car is speeded up. Sometimes an air filter is not fully sealed in its' duct and will make noise when drawing in air.

ENGINE HESITATES WHILE ACCELERATION

LOSS OF ACCELERATION

It can be fuel pressure issue or it's the problem with accelerator pedal or its clogged filters causing there.

There are many other possibilities. I suggest you to go through the list of help links mentioned below, these will help you to confirm where the actual fault lies: -------

Jerks and Hesitates During Acceleration?

http://technoanswers.blogspot.in/2012/07/2004-dodge-town-country-jerks-and.html

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Loss of acceleration?

http://technoanswers.blogspot.in/2012/02/loss-of-acceleration.html

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Headlights flickering and car hesitates to start?

http://howtobyme.blogspot.in/2012/02/headlights-flickering-and-car-hesitates.html

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How exactly the Vehicles Accelerator Cable works?

http://repairhelpcenter.blogspot.com/2011/11/how-exactly-vehicles-accelerator-cable.html

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How exactly Vehicles Accelerator Pump Diaphragm Works?

http://repairhelpcenter.blogspot.com/2011/11/how-exactly-vehicles-accelerator-pump.html

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2000 Toyota Avalon: Engine Lean Codes and Knock Sound on Acceleration?

http://whatisbyme.blogspot.in/2012/05/2000-toyota-avalon-engine-lean-codes.html

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2004 Toyota Avensis: Acceleration And Deceleration makes noise on Front End?

http://whatisbyme.blogspot.in/2012/05/2004-toyota-avensis-acceleration-and.html

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Wheel hop under hard acceleration?

http://technoanswers.blogspot.in/2012/04/wheel-hop-under-hard-acceleration.html

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2009 Chevy impala accelerator pedal sensor?

http://technoanswers.blogspot.in/2012/02/2009-chevy-impala-accelerator-pedal.html

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Nissan Pathfinder stalls and bucks on Acceleration?

http://technoanswers.blogspot.in/2012/02/nissan-pathfinder-stalls-and-bucks-on.html

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Acceleration lag problem?

http://repairhelpcenter.blogspot.com/2012/01/acceleration-lag-problem.html

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These details will help.

Thanks.

Go back to that VW dealer and complain. I'm sure you payed plenty, and I know in my shop, if a customer's car is not repaired to their satisfaction, I want to know, and make it right. Sometimes parts can be bad right out of the box, and sometimes problems are misdiagnosed. Go back, but don't agree to pay for anything untill you get a satisfactory explanation. Good luck.

Same problem happened to my 1993 Nissan 240SX SE Hatchback. Turned out to be the flywheel for some odd reason. Try that! Also in my opinion it could be bad spark plugs or a clogged fuel filter. Usually those would be the main reasons.

MISFIRE COULD BE STOPPED UP FUEL FILTER.SLOW ACCELERATE PROBLEM COULD BE TURBO CHARGER PROBLEMS.

transmission problems you may be low on fluid or it may be going bad