how does an airbag protect passengers in a car?

the airbag cushons the impact. this creates a small force over a long period of time rather than a big force over a small period fo time, this is called and impulse
 
It forms a cushion between you and the hard surface of the car windshield or roof or other parts.

The cushion decelerates the movement of your head slowly instead of all at once, as would happen without it, when your head hit the windshield.

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