When driving at over 35 mph the car jerks back and forth.
My car has 169000 miles.
My car has an automatic transmission.
Without more detail of the symptoms, there are several possibilities that could cause this. As you may know, there are a few different sensors related to the fuel delivery in your car’s intake system - one of which is the throttle position sensor. This monitors the position of your foot on the pedal relative to how much fuel is introduced into the throttle body. When this is faulty, it can cause a jerking or hesitating effect as you describe. I would suggest having an expert from YourMechanic come to your home to diagnose the hesitation problem using a scanning tool which will download the fault codes that likely registered as a result of this failing.
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