AT 20MPH MY CAR JUMPS(JERKS) IF GAS IS APPLIED HARD, DOESN'T IF APPLIED SLOWLY.

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I BOUGHT MY CAR FROM AN ELDERLY MAN, WE CHANGED THE TRANSMISSION FLUID TWICE SO FAR BECAUSE THE TRANSMISSION FLUID WAS NOT THE SYNTHETIC AS CALLED FOR IN MANUAL. WHEN I START OUT APPLYING GAS HARD THE CAR JUMPS AS IF ITS COUGHING( HARD JERK)IF I APPLY THE GAS SLOWLY IS DOESN'T DO THIS.