Math Problem Statement

A runner completes a circular lap. Why is their average velocity zero? a. They return to the starting point. b. Their speed was consistent. c. The lap took no time. d. Their path wasn't straight.

Solution

The correct answer is:

a. They return to the starting point.

Explanation:

The average velocity is defined as the displacement divided by the total time. Displacement is a vector quantity, representing the shortest straight-line distance between the starting and ending points.

  • In a circular lap, the runner starts and ends at the same point. Hence, their displacement is zero.
  • Since displacement is zero, the average velocity, which depends on displacement, also becomes zero, regardless of the total time or the speed of the runner.

Would you like further details or have questions about this concept? Here are related queries for deeper understanding:

  1. What is the difference between velocity and speed?
  2. How is average speed calculated, and why isn’t it zero for this case?
  3. Can the average velocity ever be non-zero for circular motion?
  4. How does the time taken to complete the lap influence the instantaneous velocity?
  5. What is the role of direction in determining velocity?

Tip: Always remember that velocity depends on displacement (not the path length), while speed depends on the

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Math Problem Analysis

Mathematical Concepts

Kinematics
Average Velocity
Displacement

Formulas

Average Velocity = Total Displacement / Total Time

Theorems

Displacement as a vector quantity

Suitable Grade Level

Grades 9-12