A car that stalls when accelerating is cause by the following reasons, when car stalls during cold rainy mornings with a cold engine, the problem is moisture on a distributor cap.
As you may not aware, during the night, condensation forms on the inside of distributor cap because of cold and wet weather. This moisture allows electrical current inside the distributor cap that leads to engine misfiring, this is more severe when accelerating enough to cause the car to stall. However, the formation of moisture inside the distributor cap can be avoided by parking the car inside a garage for the night if you expect to have a wet weather during the night.
When the car stalling is gradually frequent as the first time it was happened, the possible cause is that the car is suffering from a vacuum leak. Vacuum leak often start out small and gradually becomes worst due to pressure inside the car engine.
The vacuum created in the car fuel system is one of the key factor in determining how much fuel the car engine will get, any leak in the car fuel system vacuum will affect the air/fuel mixture that enters the car engine combustion chambers, this will result to car stalling.
In this case you do not have any option but to bring the car to a reputable auto repair shop and ask the mechanic to check the car for a vacuum leak, particularly the EGR and the PCV valves, as this two items are often to be the source of vacuum leak.
When car stalling is not gradually become frequent over time and also occurred not only during cold wet weather, the only possible problem of the car is a bad throttle position. Fuel injected engines have a throttle position sensor, a device which measures how far a driver pressed the gas pedal and thus the throttle. The position sensor feeds the data to the engine computer that does the calculation the resulting data is used to determine precisely how much gas the fuel injection system should inject into the engine. If the throttle position sensor provides a wrong data to the engine computer it will adversely affect the injection of gas into the engine causing the car to stall when accelerating.
Bring the car to a reputable shop and ask the mechanic to check your car throttle position sensor and repair if necessary to avoid making the car stalls while accelerating.