https://file.aiquickdraw.com/mathbot/file/1726769661930nm3ut0f7.png

To calculate the average velocity for each interval, we use the formula for average velocity:

\[
v_{\text{avg}} = \frac{\Delta x}{\Delta t}
\]

where:
- \( \Delta x \) is the change in position (displacement),
- \( \Delta t \) is the change in time.

Let's analyze each time interval using the graph you've provided:

### 1. Between 0 and 2 seconds:
From the graph:
- At \( t = 0 \), the position is \( 0 \) meters.
- At \( t = 2 \), the position is \( 8 \) meters.

So:
\[
v_{\text{avg}} = \frac{8 \, \text{m} - 0 \, \text{m}}{2 \, \text{s} - 0 \, \text{s}} = \frac{8}{2} = 4 \, \text{m/s}
\]

### 2. Between 2 and 3 seconds:
From the graph:
- At \( t = 2 \), the position is \( 8 \) meters.
- At \( t = 3 \), the position is still \( 8 \) meters (no change in position).

So:
\[
v_{\text{avg}} = \frac{8 \, \text{m} - 8 \, \text{m}}{3 \, \text{s} - 2 \, \text{s}} = \frac{0}{1} = 0 \, \text{m/s}
\]

### 3. Between 3 and 5 seconds:
From the graph:
- At \( t = 3 \), the position is \( 8 \) meters.
- At \( t = 5 \), the position is \( 20 \) meters.

So:
\[
v_{\text{avg}} = \frac{20 \, \text{m} - 8 \, \text{m}}{5 \, \text{s} - 3 \, \text{s}} = \frac{12}{2} = 6 \, \text{m/s}
\]

### 4. Between 5 and 8 seconds:
From the graph:
- At \( t = 5 \), the position is \( 20 \) meters.
- At \( t = 8 \), the position is \( 28 \) meters.

So:
\[
v_{\text{avg}} = \frac{28 \, \text{m} - 20 \, \text{m}}{8 \, \text{s} - 5 \, \text{s}} = \frac{8}{3} \approx 2.7 \, \text{m/s}
\]

### Part b: Average velocity for the overall motion (from 0 to 8 seconds):
From the graph:
- The total displacement from \( t = 0 \) to \( t = 8 \) is:
  - At \( t = 0 \), position is \( 0 \) meters.
  - At \( t = 8 \), position is \( 28 \) meters.

So the total displacement is \( 28 \, \text{m} \) and the total time is \( 8 \, \text{s} \).

\[
v_{\text{avg}} = \frac{28 \, \text{m}}{8 \, \text{s}} = 3.5 \, \text{m/s}
\]

---

### Summary:
- Between 0 and 2 s: \( 4 \, \text{m/s} \)
- Between 2 and 3 s: \( 0 \, \text{m/s} \)
- Between 3 and 5 s: \( 6 \, \text{m/s} \)
- Between 5 and 8 s: \( 2.7 \, \text{m/s} \)
- Overall average velocity: \( 3.5 \, \text{m/s} \)

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Do you want further clarification or details on these calculations?

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Here are five related questions for deeper understanding:
1. What would happen if the object had moved backward in any interval?
2. How does the slope of the graph relate to the velocity in each interval?
3. What is the difference between instantaneous velocity and average velocity?
4. How would the graph look if the object moved with constant velocity?
5. Can velocity be negative? How would that appear on the graph?

**Tip:** Average velocity depends on the total displacement, not the total distance traveled!

Calculate the average velocity of the object in motion in the following time intervals: 0-2 s, 2-3 s, 3-5 s, and 5-8 s, as well as the overall average velocity.

Learn how to calculate the average velocity of an object based on position-time graph analysis. Covers key kinematic concepts and provides step-by-step calculations for intervals such as 0-2 seconds, 2-3 seconds, and more. Suitable for high school students.

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