This happens often. To avoid the problem I gradually give it gas, but even then it doesn't solve the problem all the time.
When accelerating, it's jerking back and forth. Cuts out too at times. Why? on 2000 Mazda Millenia
Answer #1 and possible leak between throttle body and mass air flow meter (NOT the meter). Check for break(s) in hose that would be opened when stepping on throttle , because of worn engine mounts maybe?
Bet you are right, best i remember, when checking the air filter on this engine, the lube shops jack the cleaner top up about a foot to remove it breaking the hose!
Happy New Year! .......never mind.......:)
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Good tune up needed, at a repair shop!