Lets consider why air-bags can save lives.
When you travel in a car there is a large amount of kinetic
energy associated with the motion of your body with
respect to the ground. To be specific we consider
a body of mass m=70 kg traveling at v=55 mph. The corresponding
Kinetic Energy of the body with respect to the road is
This is about the energy stored in one bite of a doughnut!
If the car drives head on into a wall you are going to loose this kinetic energy
abruptly through the negative work performed on your body by forces
from parts of the car. From Eq. 3
we learned that the magnitude of the force required depends on the
distance over which the force acts. Specifically by
rearranging the expression we get
If your body slams into the dashboard the distance over which
your body is decelerated may be as small as 
m
and the force
Note that the minus sign indicates that the force does work which
reduces kinetic energy which means that the force is opposed to the
distance traversed. The max force which the body can stand depends
on the area over which it is applied. Typically if
Injury will be light. Incidentally this force is four times the
force per area unit (also called pressure) applied to the body by
the atmosphere we live in. In our crash the contact area might be just
so that
which is roughly 400 times beyond the recommended value and guarantees
serious injury.
If we use a seat belt the distance over which
the body is brought to rest can be increased to
the 0.3 m available before the dashboard and the area of contact can be
increase to 
thus
You may survive but still injuries will be heavy. If you can afford
an air-bag you are safer still mainly because the area of impact can be increased. Typically 
is limited by the space before the dashboard
but now 
so that
which is within a factor 2 of the recommended value. Note that
it is the squared speed which determined how much damage is done.
Thus you double impact damage by going from 55 mph to
55 mph=78 mph. According to this you are as safe
buckled up in
a car going 55 mph as in a car going 78 mph with air bags.