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 direction 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 speed is constant
B: her velocity changes because her direction changes
The correct statement is:
B: her velocity changes because her direction changes
In this scenario, the student first walks east and then changes her direction to the north. As her direction changes, her velocity also changes because velocity is a vector quantity that considers both speed and direction. Therefore, statement B is the most accurate.
To determine which statement is true, let's first understand the concepts of velocity, speed, and the relationship between direction and velocity.
Velocity is a vector quantity, meaning it has both magnitude (speed) and direction. Speed, on the other hand, is a scalar quantity, representing only the magnitude.
Now, let's analyze the situation described in the question. The student initially walks east for 100 meters in 2 minutes. This means her speed can be calculated as 100 meters / 2 minutes = 50 meters per minute. Similarly, for her second motion, she walks north for 200 meters in 4 minutes. Her speed in this case is calculated as 200 meters / 4 minutes = 50 meters per minute as well.
Since the student's scalar speed remains constant, we can conclude that her speed is constant (as stated in statement D). However, velocity also takes into account the direction. In this case, the student changes her direction from east to north.
Therefore, the correct statement is B: her velocity changes because her direction changes. While her speed remains the same, her velocity changes because the direction in which she is moving changes.