I am a high school student and I was studying kinematics about position of a body. So, one thing I do not understand in this diagram is the position of woman. Initally, at $t=0$, this woman was at $x=1.5\,\text{m}$ from reference frame; but her hands, her legs or any point of the woman are at different positions. So how we can say that this woman is at $x=1.5\,\text{m}$? How we can define the position of the woman?
A good, fundamental question.
Position is a point-measure. But the woman is not a point. Rather, as an extended geometric object she spans over/consists of many, many different points. She is a so-called continuous object. To state her position you can only state the position of a chosen point within her.
Which point should we choose? Can we pick a point that reasonably can represent the woman, if we have to represent her by just one point?
Physicists will often model an object as "point-like" in cases like this where the shape is not relevant, and then choose such a point to represent it. Typically they will choose the point to be the centre of mass.
All that being said, in your textbook example here I would not presume much precision in the choice of point. Most likely they simply refer to an intuitive, inaccurate idea of what where means. Which would be fine for introductory explanations.
A great question, and classic anecdotal validation of my number one rule of pedagogy:
"No physics principle is clarified by including the human body."
-JEB
So I blame whomever green lit the text book.
Nevertheless, it's a great opportunity to apply the Method of The Spherical Cow (https://en.wikipedia.org/wiki/Spherical_cow); however, in this case, you would use the Spherical Woman.
In many physics problems, we treat a real physical body as a zero-size point mass that exists at the position of the center of mass. When we say that a body has moved through some distance, it should usually be interpreted as meaning the body's center of mass has moved that distance. Although the woman's arms and legs may be in different positions and may each have moved more or less than 2m, the net effect is that her center of mass has moved by 2m.
You are correct that we are using imprecise terminology when we say a person moved 1.5m. in the strictest sense, a person cannot move some measures distance, only a point can. We would need to specify which point we are talking about. We may say the point at the tip of her thumb moved 2m, since it does look like it moved further than the rest of her.
Every object has a special point, called it's center of mass. This is a very special point in physics because in many calculations regarding distributed forces, we can act as if they all acted upon that one point. This greatly simplifies calculations to the degree that we may start to be imprecise and say the position of the teacher's center of mass is her position.
So it's a reasonable assumption when people talk about a person's position to assume they are talking about their center of mass (which is right around belly button level in the centerline of the torso).
But it's good to check. If this were a robotics problem, "her position" may refer to a point on her feet. Many robotics problems deal with reachability and the extent of her reach is defined by where she is standing.
