Question

question 13.
emily is conducting an experiment to compare the speed and velocity of two runners. she tracks how long it takes each runner to complete a 200 - meter straight track. runner a runs the track in a straight line, while runner b runs the same distance but zigzags across the track.
what is the key difference between speed and velocity in this situation?
a. ○ speed depends on the total distance traveled, while velocity depends on the displacement and direction.
b. ○ speed depends only on the direction of motion, while velocity depends on the total distance traveled without direction.
c. ○ speed and velocity are the same for both runners since they cover the same distance in the same time.
d. ○ velocity can be calculated using distance, while speed depends on displacement and direction.

Explanation:

To determine the key difference between speed and velocity, recall their definitions:

• Speed is a scalar quantity, defined as the total distance traveled divided by time (\( \text{Speed} = \frac{\text{Total Distance}}{\text{Time}} \)), with no regard for direction.
• Velocity is a vector quantity, defined as displacement (straight - line distance from start to end, with direction) divided by time (\( \text{Velocity} = \frac{\text{Displacement}}{\text{Time}} \)), so it depends on both displacement and direction.

Now analyze the options:

• Option A: Matches the definitions (speed depends on total distance; velocity depends on displacement + direction).
• Option B: Incorrect. Speed has no dependence on direction, and velocity depends on displacement (with direction), not total distance.
• Option C: Incorrect. Velocity depends on direction (Runner B’s displacement is shorter than Runner A’s since B zigzags), so their velocities differ.
• Option D: Incorrect. The relationship is reversed: speed uses distance, velocity uses displacement.

Answer:

A. Speed depends on the total distance traveled, while velocity depends on the displacement and direction.