A student walks east 100 meters in 2 minutes. She then walks north 200 meters in 4 minutes. Which statement is true?
Her velocity changes because her speed varies.
Her velocity is constant because her direction is constant.
Her velocity changes because her direction changes.
Her velocity is constant because her speed is constant.
Her velocity changes because her direction changes.
The correct statement is: Her velocity changes because her direction changes.
Velocity is a vector quantity that takes into account both speed and direction. To determine the velocity of the student at each leg of her journey, we need to calculate the average velocity for each segment.
Speed is determined by dividing the distance traveled by the time taken, and it represents the magnitude of velocity.
For the first segment, the student walks east 100 meters in 2 minutes. Therefore, her speed is 100 meters / 2 minutes = 50 meters per minute. However, we also need to consider the direction. Since she is walking east, her velocity for this segment is 50 meters per minute eastward, or +50 m/min in vector notation.
For the second segment, the student walks north 200 meters in 4 minutes. Her speed for this segment is 200 meters / 4 minutes = 50 meters per minute, which is the same as the first segment. However, the direction has changed to north. Thus, her velocity for this segment is 50 meters per minute northward, or +50 m/min in vector notation.
Comparing the two statements provided:
1. "Her velocity changes because her speed varies." - This statement is not true because her speed remains constant at 50 meters per minute for both segments.
2. "Her velocity is constant because her direction is constant." - This statement is not true because her direction changes from east to north.
3. "Her velocity changes because her direction changes." - This statement is true because the change in her direction results in a change in her velocity, even though her speed remains constant.
4. "Her velocity is constant because her speed is constant." - This statement is not true because her velocity changes due to the change in direction, even though her speed remains constant.
Therefore, the correct statement is: "Her velocity changes because her direction changes."