It is because of newton's third law ......
According to this law , every action has an equal and opposite reaction .
Therefore , when a gun is shot ( here the action force ) , the bullet is fired out (released) from the gun with a high force . As a result the gun has to produce equal and opposite reaction . As a result , the gun jerks back .......
In order to reduce the " recoil " of the gun ,the mass of the gun is increased .
B>>
The belt itself do not stretch. However the seat belt is made to slack, this is for the user to adjust the belt base on the user's body size and comfort. The belt should be snug fit, and should be tested by forceful tugging it to see if the locking mechanism works.
At the moment of vehicular impact the sudden deceleration has tremendous G-Force, which without the allowable slack can cause serious injury above the injury one can sustain from the cab crashing inward towards the passenger, this slack allows the mechanism to engage at a specific G-Force. The head rest also plays a vital role in vehicular crash safety, without it accidents can cause whiplash effect on the neck and break it.
Slack in the seat belt also somehow cushion the blow, while the seat belt portion around the waist, holds the passenger in place, as the force can cause the passenger to be thrown out the window.
C>>
Law of inertia is also known as Newton's first law of motion which states that a body continues to be in a state of rest and in continuous motion until unless an external force is applied on it. The dust particles are in a state of rest until beaten with a stick( here external force is beating of stick on carpet).