Answer
See the detailed answer below.
Work Step by Step
a)
When the car is moving at a constant speed the only forces exerted on the described passenger are the normal force from the chair and the gravitational force due to Earth's gravitational pull (recall that the author told us that his chair has no back and is perfectly frictionless).
b)
This means that the net force exerted on him is zero.
c) and d) Now the car is slowing down, and the passenger's body wants to maintain its original state of moving forward at a constant speed and since the chair is frictionless, he will start sliding forward on the chair. So, he is actually still, momentarily, moving at the same constant speed. Thus, the forces exerted on him are the same and the net force exerted on him is still zero.
Therefore, we have the same force diagram as parts a and b.
e) According to Newton's first law, all bodies attend to maintain their original state. So, you are throwing forward since your body is maintaining its original state of moving forward at a constant speed. So actually there are no forces pushing you forward at all.
f) Now we have a friendly chair that will save the passenger from throwing forward when the car slows down or suddenly stops. It has the greatest force in the world, the friction force.
And since we know that the passenger is on the verge of sliding forward, then the friction force must be opposing his motion direction. This means that the static friction force between the passenger's body and the chair had to be backward, see the figures below.
Hence, the force that is the cause of the slowing down of the passenger is the static friction force $F_s$.
