Math Problem Statement

David runs exactly 2 laps around a 400m track. What is his distance and displacement?

Solution

David runs 2 laps around a 400m track.

  • Distance: Distance is the total length traveled. Since each lap is 400 meters, and David runs 2 laps: Distance=2×400=800meters\text{Distance} = 2 \times 400 = 800 \, \text{meters} So, his distance is 800 meters.

  • Displacement: Displacement is the shortest straight-line distance between the start and finish points. Since David returns to his starting point after completing the laps, his displacement is: Displacement=0meters\text{Displacement} = 0 \, \text{meters} because there is no change in position.

Would you like more details or have any further questions?

Here are some related questions:

  1. How would the displacement change if David stopped halfway through the second lap?
  2. What is the difference between distance and displacement in terms of direction?
  3. How do you calculate displacement in a circular motion for a partial lap?
  4. How does average velocity differ from speed in this scenario?
  5. What would be David's displacement if he ran one full lap and then half of another?

Tip: In circular motion, displacement can be tricky—always consider the start and end points to determine it!

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Math Problem Analysis

Mathematical Concepts

Distance
Displacement
Circular Motion

Formulas

Distance = number of laps × length of one lap
Displacement = straight-line distance between start and end points

Theorems

Concept of displacement in circular motion

Suitable Grade Level

Grades 6-8