For his early morning exercise, Andee jogged 12 times around a circular track of radius 5.0 m. Find his total distance traveled and his displacement.$$  $$

To solve this problem, we need to calculate both the total distance Andee traveled and his displacement.

### 1. Total Distance Traveled
The total distance Andee jogged can be calculated by first determining the distance for one complete lap around the circular track, which is the circumference of the circle.

The formula for the circumference $ C $ of a circle is:

\[
C = 2\pi r
\]

Where:
- $ r $ is the radius of the circle,
- $ \pi $ is approximately 3.14159.

Given:
- $ r = 5.0 $ meters

So, the circumference $ C $ is:

\[
C = 2\pi(5.0 \, \text{m}) = 10\pi \, \text{m} \approx 31.42 \, \text{m}
\]

Since Andee jogged 12 laps, the total distance $ D $ he traveled is:

\[
D = 12 \times 31.42 \, \text{m} \approx 377.04 \, \text{m}
\]

### 2. Displacement
Displacement is a vector quantity that refers to the change in position from the starting point to the ending point. Since Andee jogged 12 complete laps and ended up at the same point where he started, his displacement is:

\[
\text{Displacement} = 0 \, \text{m}
\]

### Summary:
- **Total Distance Traveled:** $ \approx 377.04 \, \text{m} $
- **Displacement:** $ 0 \, \text{m} $

Would you like more details on any part of this solution? Here are some related questions:

1. How do you calculate the circumference of any circle?
2. What is the difference between distance and displacement?
3. If Andee jogged only half of a lap, what would his displacement be?
4. Can displacement ever be greater than distance?
5. What factors can affect the displacement in circular motion?

**Tip:** Displacement considers only the initial and final positions, not the path taken.

For his early morning exercise, Andee jogged 12 times around a circular track of radius 5.0 m. Find his total distance traveled and his displacement.

Explore how to calculate the total distance traveled and displacement for an athlete jogging 12 laps around a circular track with a 5.0m radius. This problem involves key concepts in geometry and circular motion, suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation