# A car moving at constant speed is suddenly braked. The occupants, all wearing seat belts, are...

## Question:

A car moving at constant speed is suddenly braked. The occupants, all wearing seat belts, are thrown forward. The instant the car stops however, the occupants are all jerked backward. Why? Is it possible to stop an automobile without this jerk?

## Accelerated Frames Of Reference

In a frame of reference moving with constant velocity, Newton's laws of motion may be directly applied for analyzing the motion. Such frames of reference are called inertial frames. On the other hand, the velocity of a non-inertial frame keeps changing. Now fictitious or pseudo forces should be incorporated before applying Newton's laws when analyzing motion within the non-inertial frame.

If the acceleration of a non-inertial frame is {eq}\displaystyle {a} {/eq} then an object of mass {eq}\displaystyle {m} {/eq} will experience a fictitious force {eq}\displaystyle {- m a} {/eq}.

Clearly this force arises on account of the inertia of the object since it depends on the mass. Hence it is also called an inertial force. If this is included over and above the contact and long-range forces then Newton's second law will give the correct acceleration as measured in the non-inertial frame.

If you are inside a car that is moving uniformly then no fictitious force is experienced. But if the car brakes suddenly then the car experiences a backward acceleration. Then all objects in the car frame of reference will experience a fictitious force that is directed forward. This is the reason why you are thrown forward when the car brakes suddenly.

Now if the person is wearing a seat belt the belt will hold him or her in place by exerting a reaction force that matches the forward-directed fictitious force. The moment the car stops, the fictitious force vanishes but the seat belt takes some time to respond and relax to its original state. Hence now the only force is the reaction of the belt pressing the person back. This is the reason for the jerk back after coming to a stop. The jerk can be minimized if the car doesn't stop but keeps going backwards.

Similarly, when the car starts from rest it experiences a forward acceleration. Therefore a person inside the car will experience a fictitious force acting backward. The effect of the fictitious force can be minimized by accelerating slowly over a longer period of time to attain the desired velocity.