Solution

While the car is accelerating, it is the opposite way round. The inert air impounds at the rear end of the car. Thus the pressure in the back is higher than in the front which causes the correspondent, different force. Therefore the balloon is pushed forward while the car is accelerating.

You can observe a similar behaviour of the balloon in curves. In what direction does the balloon move during a right hand bend and in what direction does it move during a left hand bend?