https://file.aiquickdraw.com/mathbot/file/1724875521566mney2ieu.jpg

C. What is the object's maximum acceleration? Explain how you found this.

To determine the object's maximum acceleration from the graph, we need to analyze the slope of the velocity-time graph because acceleration is the rate of change of velocity with respect to time. The steeper the slope, the greater the acceleration.

### Steps to Find Maximum Acceleration:
1. **Identify the sections of the graph:**
   - The graph has three distinct linear segments:
     - **Segment 1:** From \( t = 0 \) to \( t = 2 \) seconds, the velocity increases.
     - **Segment 2:** From \( t = 2 \) to \( t = 4 \) seconds, the velocity is constant.
     - **Segment 3:** From \( t = 4 \) to \( t = 6 \) seconds, the velocity decreases.

2. **Calculate the slope of each segment:**
   - **Segment 1 (0 to 2 seconds):**
     - Initial velocity (\(v_1\)) = 0 m/s
     - Final velocity (\(v_2\)) = 4 m/s
     - Time interval (\( \Delta t \)) = 2 s
     - Acceleration \( a_1 \) = \( \frac{v_2 - v_1}{\Delta t} = \frac{4 - 0}{2} = 2 \) m/s²
   - **Segment 2 (2 to 4 seconds):**
     - The velocity is constant (no change), so acceleration \( a_2 = 0 \) m/s².
   - **Segment 3 (4 to 6 seconds):**
     - Initial velocity (\(v_3\)) = 4 m/s
     - Final velocity (\(v_4\)) = -2 m/s
     - Time interval (\( \Delta t \)) = 2 s
     - Acceleration \( a_3 \) = \( \frac{v_4 - v_3}{\Delta t} = \frac{-2 - 4}{2} = -3 \) m/s²

### Conclusion:
- The maximum acceleration in magnitude occurs in **Segment 3** and is \( -3 \) m/s². Although it's negative (indicating deceleration), the magnitude \( |a_3| = 3 \) m/s² is the largest.

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

1. What does the negative acceleration in Segment 3 indicate about the object's motion?
2. How does constant velocity in Segment 2 affect the object's acceleration?
3. What is the significance of the slope in a velocity-time graph?
4. How would the graph look if the object had constant acceleration?
5. Can you determine the total displacement of the object using this graph?

**Tip:** Remember that the steeper the slope in a velocity-time graph, the greater the acceleration (positive or negative).

Explore how to determine an object's maximum acceleration from a velocity-time graph. Learn about analyzing slopes, calculating acceleration, and interpreting motion segments. Suitable for high school physics students.

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