91Ó°ÊÓ

Displacement is a term that often comes up in physics problems, particularly when dealing with motion. It refers to the change in position of an object and is a vector quantity, which means it has both magnitude and direction.

For instance, if a student travels from her home to the university, her displacement would be the straight-line distance between these two points, regardless of the actual path taken. Even if the car's odometer reads 12.0 km, the displacement might be different, precisely because it's the straight-line distance. In the example given, the displacement is reported as being 10.3 km in a specific direction (25.0° south of east). Understanding displacement is critical for analyzing motion correctly, as it differs from the total path length.

Physics problems often distinguish between scalar and vector quantities. A vector quantity includes both a magnitude and a direction, which makes it different from a scalar quantity that only has a magnitude. Speed is a scalar quantity, as it merely tells you how fast an object is moving, without considering its direction.

In contrast, velocity is a vector quantity as it describes the speed of the object in a particular direction. This is why when we discuss average velocity, we must account for both how fast the object has moved and in which direction. In the given scenario, while calculating the average velocity of the student's trip to the university, the direction specified was crucial to establish the velocity as a vector.

The average velocity is obtained by dividing the displacement by the total time taken for the trip. Because displacement is a vector, the average velocity is also a vector, reflecting both the rate and the direction of travel.

In our problem's context, to calculate the student’s average velocity on her way to the university, you take her displacement (10.3 km at 25.0° south of east) and divide it by the total travel time converted into hours (18.0 minutes or 0.3 hours). This calculation gives a concise description of her motion that includes not just how fast she traveled, but also her travel direction.

When calculating speed or velocity, ensuring consistent units is vital for an accurate result. Often, you'll need to convert time from minutes to hours, since speed is typically expressed in kilometers per hour (km/h).

To convert minutes to hours, divide the number of minutes by 60, because 1 hour equals 60 minutes. This step is critical when you work with physics problems that give you time in minutes, but ask for speed in km/h. In our example, to find the average speed, we convert 18 minutes to hours by dividing by 60, obtaining 0.3 hours, and then proceed with the speed calculation.

In physics, the relationship between distance, speed, and time is fundamental. The basic formula connecting these quantities is Speed = Distance / Time. This formula holds true for constant speed, but if the speed is not constant, you would have to use the average speed definition.

In our exercise, understanding this relationship enables us to calculate the student's average speed by dividing the distance her car's odometer increased (12.0 km) by the total time of the trip (0.3 hours). Similarly, the average speed for the complete round trip takes into account the total distance traveled back and forth and the total time including delays, such as the 7 hours and 30 minutes spent at the university before returning home.