What is more harmful in a car crash - restrciting movement or allowing some movement to reduce g-force?

The short answer to the question as posed in the title to your post is both.

The purpose of the seatbelt is to restrain you so that you stop with the car thereby making your stopping distance the same as the car and greater than if you had no seatbelt. Without the seat belt your inertia keeps you moving forward at the same velocity until you impact an object in the car which then stops you. You are then at the mercy of how much "give" the object has since that will determine your stopping distance.

A crash which stops the car and driver must take away all its kinetic energy according to the work energy principle which states that the net work done on an object equals its change in kinetic energy, or


Where $F_{ave}$ = the average force you experience.

$d$ = your (and the vehicles) stopping distance.

$m$ = your mass

$v$ = your (and vehicle) relative velocity with wall before the crash

The vehicles crumple zone, seat belts, and air bags are all designed to increase your stopping distance and/or absorb the energy of the impact.

On the other hand, seat belts with a moderate amount of stretch further increases the stopping distance of the occupant, additionally reducing the average force experienced by the occupant while still restraining the occupant from impacting the objects within the vehicle.

Hope this helps.

A body in motion has an inertia of motion by virtue of which it tries to maintain it's previous state of motion(both speed and direction). For example it is noticed that on suddenly applying brakes to stop we are jerked in forward direction which is due to the inertia of motion.

Now when we are in enclosed space we must take care of the fact that if we don't stop, relative to the nearby objects, then it is quite probable that we may get hurt. So what to do then? Answer is to somehow attach ourselves to the surrounding so that when they stop our body stops with the them. But there is another problem which is of the case that on making our body to stop suddenly by applying constraints causes a lot of force on our body which can cause minor/sever damage and can be lethal.

So what should we do then?

The right thing is the case which is somewhere inbetween i.e., to make our bodies stop in such amount of time that a comparatively lesser force acts on us but we stop in such distance that our head or other part doesn't collide with the nearby object. So my suggestion is to do the thing in which both are satisfied.

$$\pmb {\underline {\text {Further Reading }}}$$

  • The Statistics: Car Safety and Pets in America

  • How to Keep Your Pets Safe When Traveling

  • Pet Travel Safety - How To Travel Long Distance | American Red Cross

  • Travel Safety Tips | ASPCA

When your car drives head-on into an unyielding obstacle, the front end of the car will absorb energy by "crumpling." The relatively rigid passenger compartment will take somewhat more time to come to a stop than the front bumper will take, and so the passenger compartment and anything that is rigidly attached to the passenger compartment will experience a lower peak acceleration than the front bumper will experience.

Instead of a car, Let's imagine a bus that runs head on into a wall while traveling at 60 miles per hour, with your dog on the back seat. If your dog is not strapped in, then as the bus starts to crumple, your dog will continue at 60 miles per hour, flying through the air, until it impacts the front of the bus, which likely will have come to a compete stop by that time. But, if your dog is strapped in to the back seat, then it, and the back seat, will slow down more gently while the front of the bus is crumpling.

The difference might not be as great in a shorter car, but I'd still rather be strapped in than not.

P.S., When the police officer looked at me, sitting unhurt on the grass next to the wreck of my car he said, "I don't need to ask whether you were wearing your seat belt." I guess he'd seen enough people who were and enough who weren't to be able to tell the difference.