I have a Hyundai Getz (not in the list) 2004.
Occasionally when driving and I have to stop (junction, traffic etc.), as I try to pull away the car has no/very little power. In 1st, with my pedal to the floor, the engine does not rev up, but it doesn't stall either. The car will still move but as a snail's pace, even up a steep hill. After 20-30 seconds the problem corrects itself and the car revs and speeds up normally. Car is serviced annually, this problem occurred before and after servicing. Timing belt is overdue for replacement. Central and rear exhaust have been replaced in the last few years and I believe the fuel filter was changed on the last servicing.
My car has 79000 miles.
My car has a manual transmission.
There are a number of things that may cause the car to hesitate when accelerating such as low fuel pressure, a dirty or faulty mass air flow sensor, clogged or dirty fuel injectors, a faulty throttle position sensor or potentially a bad fuel pump. I would recommend having a professional from YourMechanic come to your location to diagnose and inspect your vehicle.
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