A student walks east 100 meters in 2 minutes. She then walks north 200 meters in 4 minutes. Which statement is true?
A Her velocity is constant because her speed is constant.
B Her velocity changes because her direction changes.
C Her velocity changes because her speed varies.
D Her velocity is constant because her direction is constant.
B Her velocity changes because her direction changes.
The correct statement is B) Her velocity changes because her direction changes.
Velocity is a vector quantity that includes both speed and direction. In this scenario, the student walks first east and then north, which means her direction changes. Therefore, her velocity changes as well since velocity takes into account both speed and direction.
To determine which statement is true, we need to understand the concepts of speed and velocity. Speed is a scalar quantity that only considers the magnitude of an object's motion, while velocity is a vector quantity that takes into account both the magnitude (speed) and direction of the motion.
In this scenario, let's break down the student's motion:
- Walking east 100 meters in 2 minutes: The student is moving along the x-axis in the positive direction (east) for a distance of 100 meters in a time of 2 minutes. Therefore, the speed is calculated as 100 meters / 2 minutes = 50 meters per minute. The velocity is 50 meters per minute in the positive x-direction.
- Walking north 200 meters in 4 minutes: The student is now moving along the y-axis in the positive direction (north) for a distance of 200 meters in a time of 4 minutes. Again, we calculate the speed as 200 meters / 4 minutes = 50 meters per minute. The velocity is 50 meters per minute in the positive y-direction.
Analyzing the above information, we can conclude that the student's velocity changes because her direction changes (from east to north). Therefore, the correct statement is:
B Her velocity changes because her direction changes.