https://file.aiquickdraw.com/mathbot/file/1726553287543u3jtw5ot.jpg

Let's analyze the problem and extract the required information to solve it.

### Problem Breakdown:
- **Diagram**: The diagram shows an oval racetrack. There are 3 positions marked: Position 1, Position 2, and Position 3. The car starts at "Start."
- **Distances**:
  - The **oval distances** from Start to each position around the track are:
    - Start → Position 1: 400 m
    - Start → Position 2: 520 m
    - Start → Position 3: 400 m
  - **Straight-line distances** (dashed lines):
    - Start → Position 1: 290 m
    - Start → Position 2: 520 m
    - Start → Position 3: 290 m

### To Calculate:
We are to fill in the table with:
1. The **distance** (d) from Start to each position around the track.
2. The **displacement** (Δx), which is the straight-line distance from Start to each position.

### Solution:

- **Start → Position 1**:
  - Distance \( d = 400 \, \text{m} \) (following the track)
  - Displacement \( \Delta x = 290 \, \text{m} \) (straight-line distance)

- **Start → Position 2**:
  - Distance \( d = 520 \, \text{m} \)
  - Displacement \( \Delta x = 520 \, \text{m} \) (straight-line distance)

- **Start → Position 3**:
  - Distance \( d = 400 \, \text{m} \)
  - Displacement \( \Delta x = 290 \, \text{m} \)

- **Start → Start** (completing the loop):
  - Distance \( d = 0 \, \text{m} \) (no motion)
  - Displacement \( \Delta x = 0 \, \text{m} \) (same starting and ending point)

### Completed Table:
| **Route**             | **Distance (d)** | **Displacement (Δx)** |
|-----------------------|------------------|-----------------------|
| Start → Position 1     | 400 m            | 290 m                 |
| Start → Position 2     | 520 m            | 520 m                 |
| Start → Position 3     | 400 m            | 290 m                 |
| Start → Start          | 0 m              | 0 m                   |

---

Would you like more details or explanations on how displacement and distance differ in this case?

Here are 5 follow-up questions to consider:
1. How would the displacements change if the positions were in different locations?
2. What is the total distance traveled if a car completes a full lap from Start back to Start?
3. What would happen to the displacement if a car moved clockwise instead of counterclockwise?
4. How would you calculate average speed if given a time to travel between Start and Position 2?
5. How does the concept of displacement change when considering a 3D track?

**Tip:** Remember, displacement depends only on the initial and final positions, while distance depends on the path taken.

Using the diagram, determine the distances and displacements for a car moving from Start to Position 1, Start to Position 2, Start to Position 3, and back to Start.

This problem involves calculating the distance and displacement for a car traveling along an oval racetrack. The diagram provides various distances, and users are asked to differentiate between distance (path length) and displacement (straight-line distance). Key concepts include motion physics and vector direction, suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation