You apply the brakes of your car abruptly and your book starts sliding off the front seat. Three observers sitting in the car explain this differently. Observer A says that the book continued moving and the car accelerated from underneath it. Observer B says that the car pushed forward on the book. Observer C says that she must be in a noninertial reference frame because the book started moving without any extra objects interacting with it. Which of the observers is correct? Assume that the car is a frame of reference of all observers.

All the observers are correct.

Explanation:

This is simply a problem of reference frames from which the motion of the book is being viewed by the various observers.

From their various reference frames, they are all correct.

Observer A must be in the inertial reference frame.

Observers who can explain the behavior of the book  and the car by using the relationship between the sum of  the forces and changing velocity are said to be observers in inertial reference frames.

This is clearly shown by what observer A noticed. There was a relative motion between the book and the car as she pointed out, making her to be in an inertial reference frame.

Similarly, observers in inertial reference frames can also explain the changes in velocity of objects  by considering the forces exerted on them by other objects.

This is shown by observer B as he is able to notice how the force of the car affects the velocity of the book.

Observer C is actually in a non-inertial reference frame, as newtons law of force motion relationship are no longer observed. This occurs in the non inertial reference frame.