Final answer:
The woman's average velocity is -0.82 m/s to the south, taking into account that velocity is a vector quantity and the negative sign indicates the direction.
Step-by-step explanation:
To calculate the woman's average velocity during her entire motion, one needs to consider the total displacement over the total time. Displacement is a vector quantity, meaning it has both magnitude and direction. Since the woman walks south and then turns to walk north, the displacements in these two legs of the trip will partially cancel out. For the first part of the trip, she walks 2.00 m/s for 60.0 minutes (3600 seconds), resulting in a displacement of 7200 m south. After turning around, she walks 3000 m north. The total displacement is then 7200 m - 3000 m = 4200 m to the south (negative displacement due to the direction). The total time taken is 60.0 minutes + 25.0 minutes which is 85.0 minutes (or 5100 seconds). The average velocity is hence the total displacement divided by the total time: -4200 m / 5100 s = -0.82 m/s (the negative sign indicates the southward direction).