Final answer:
The false statement mixes up distance with displacement. Distance is a scalar and requires only magnitude, while displacement is a vector, requiring both magnitude and direction. The correct statement for distance traveled would omit direction and be simply "25 m."
Step-by-step explanation:
The statement "25 m east would be the correct way to represent the distance traveled by a woman moving to the east 25 meters" is false because distance is a scalar quantity and only requires a magnitude for its description, without any direction. The correct representation would be simply "25 m." However, the statement may be trying to express displacement, which is a vector quantity and includes both magnitude and direction. Therefore, if the intent is to describe the displacement, the statement would be correct. But as for distance, mentioning "east" is unnecessary.
To illustrate this concept with respect to displacement, consider a woman walking from point A to point B in a city with square blocks. The woman taking the path from A to B may walk east for so many blocks and then north (two perpendicular directions) for another set of blocks to arrive at B. How far she walks east only depends on her motion eastward, and how far she walks north depends only on her motion northward.
When calculating displacement, the direction is critical because displacement is defined as the vector that stretches straight from the starting point to the endpoint, regardless of the path taken. In this case, if the woman walked 25 m east, her displacement would indeed be 25 m to the east. However, if discussing distance only, the direction does not matter, as it is not a vector quantity.