If this happens only in the morning the culprit may be moisture in the distributor cap. Why? During the night condensation or moisture can form on the inside of the distributor cap. This is due to cold and wet weather and the fact that the engine is cold. This moisture allows electrical current to arc inside the distributor cap and this arcing causes the engine to misfire. During acceleration this misfire gets so extreme it can cause the engine to stall.
If this problem has slowly gotten worse over time then a vacuum leak could be the cause. Why? Vacuum leaks typically start out small almost unnoticeable and gradually become worse due to heat and pressure inside the engine. Any leak in a fuel system’s vacuum will intermittently throw off the air/fuel mixture that enters the engines combustion chamber. This results in a hesitation, jerking or in extreme situations, stalling.