Lets understand what is happening here. First drive along in your car at 60 km/h on a backstreet with no traffic, then brake gently and slowly. You will notice that the seat belt doesn't really do much to hold your body. Now do the same again but this time break as quickly and sharply as you can. Your body will be thrown forwards with great force, and your seatbelt will be literally holding you in place. .
Now your body was what is commonly referred to as being "thrown forwards", however this is not the case. Your body was actually not slowing down much at all and your velocity relative to the car initially was much greater. The car began to slow down due to breaking and your body in accordance with Newtons First law wanted to continue to move at the original constant velocity. Now if your seat belt was not there to provide an opposing force, to your momentum and inertia, by holding you from going forwards, you very likely would have been thrown into the dash or steering wheel. .
Lets look at this mathematically. .
m= your mass in kilograms for this purposes 70kg .
V= final velocity 0 m/s .
U= initial velocity 60 km/h or 16.6 m/s straight line .
S= distance taken to stop 42 m .
t= 3.8 .
a= -4.368 m/s/s .
Now your momentum at 60km/h is P=MU .
So P= 70kg*16.6m/s .
P=1162 Kg m/s .
Impulse I=MU/t .
I=70*16.6/3.8 .
I=305N .
So your body will weigh about 610kg when you are breaking hard, a force it is difficult for any person to withstand. .
Now in the context of a head on accident at around 60km/hr the force exerted on your body is greatly increased. In the event of such an accident it will take the car approximately 0.4 seconds to stop. This gives an acceleration of1.5m/s/s. This means the impulse on your body would be equal to: .
I=MU/t .
I=70*16.6/0.4 .
I=2905N .
So your body would weigh around 300kg. .
With this amount of inertial force it is impossible for anyone not wearing a seatbelt to stay in his or her seat. They will either be thrown forwards into the dash or steering wheel, with a force that is capable of crushing skulls or rib cages.
