The girl in the image walks along the balance beam with her arms out to her balance. why does she do this?

So that a better balance can be obtained

Explanation:

When she lifts his arms she causes her center of gravity to rise, and the further away the center of gravity from the point of rotation (her feet), the greater the rotational inertia will be and it will swing slower allowing more time to adjust and thus be able to maintain the balance easily.

Another example of this case is when we are balancing a body in the extreme of a rod with our fingers, as we can see in the attached image.

Another example of this case is when we are balancing a body at the end of a rod with our fingers. The further the center of gravity of the rotation point (in this case the finger tip), the greater the rotational inertia and the rod will swing more slowly.

Is a  vector quantity  that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.

Independent variable is something that is changed in a experiment.