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I had this in my final year HSC physics paper at high school, only if was skewed to a left and right scenario.
If the car swerves left, inertia sees the air wish to continue on the original vector - which with a car swerving left around it would "bunch up" on the RHS of the car. Higher pressure there would see the balloon tend left - towards the direction of travel.
Hence, in the fore/aft version here, under braking we'd theoretically see higher air pressure at the front of the car - pushing the lighter density object away - which is rearwards.
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