During a head-on collision, a 22 kg child in the front seat of a car accelerates from 13.7 m/s (≈ 30 miles/hour) to 0 m/s.
The driver of the car holds out his arm to keep his child (who is not wearing a seat belt) from smashing into the dashboard.
If he can stop the kid, he'll do it by exerting a force over a distance of about 1 m.
(a) What is the acceleration of the child during this stopping motion?
(b) What is the magnitude of the force his arm must exert on the child?

Question

anonymous · Answer

The father can't really handle this force, so the dashboard does the stopping.
It will do so by exerting a force over a distance of about 0.049 m (the radius of the kids head).
(c) What will the child's acceleration be in this case? 
(d) What force will the dashboard exert on the child?
Suppose, instead of the scenarios above, that the kid was wearing a seatbelt.
The belt has some 'give' to it, so the force required to stop the kid is exerted over a distance of 0.29 m.
(e) What force will the belt exert on the child?