Question

Why are car seat belts designed to stretch somewhat in the collision?

Answer 1

Car seat-belts are designed to be stretchable, as stretching the seat-belt allows the large momentum of a passenger to reduce gently and the passenger is prevented from being thrown forward violently. Therefore, major injuries can be prevented if the car suffers a collision.
Seat-belt prevents the occupant from colliding with the interior parts of the vehicle. Reduce the risk of being thrown from the vehicle. In modern cars, seat belts are designed to work together with airbags. In a crash, the seat belt slows the speed of occupants so they impact safely with the airbag.

Formula used:
$P \propto \dfrac{1}{t}$
Where,
$P$ = momentum
$t$ = time

Complete step by step answer:
All the cars are provided with seat belts to prevent accidents. The job of the seat belts is to hold the passenger in place so the passenger is almost part of the car which prevents the passenger from flying forward as the car stops abruptly in the case of a collision. It is to prevent injuries in case of an accident by increasing the time taken by the passenger to fall forward.
When a car is moving at a high velocity its momentum is also high and people in the car also have the same momentum. We know momentum is inversely proportional to time. So if the momentum is brought to $0$ at a short time then the force acting on a body is large.
So, when a car meets an accident the person falling in front with the presents of stretchable seat belts as elastic seat belts reduces the momentum in more time to reduce the force.
So, by stretching somewhat the seat belt allows the large momentum of a passenger to reduce gently, the passenger is prevented from being thrown forward violently and injury is prevented during a collision.

Note: A seat belt is a vehicle safety device designed to secure the driver or passenger against a collision.
It exerts equal and opposite force on the body when the body tends to move in the forward direction.
Momentum is inversely proportional to time.