Airbags are the most important safety feature in cars. They don't change the rate of acceleration: the car comes to a halt at the same speed, therefore, the person inside does as well.
No, they absolutely do change the rate at which the person inside stops: most importantly they affect the amount of time it takes for their head to stop moving, by starting to decelerate it before it hits the dashboard (the seatbelts also contribute to this).
In other words they change the rate of change of the acceleration. We call that derivative jerk. Jerk is responsible for the shockwave which would otherwise rattle the brain around, it's also the chief factor in producing whiplash.