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find the average velocity from t-10s and t=20s show all work

To find the **average velocity** between \( t = 10 \) seconds and \( t = 20 \) seconds, we use the following formula:

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

Where:
- \( \Delta x \) is the change in position (in meters) over the time interval.
- \( \Delta t \) is the change in time (in seconds).

### Step-by-Step Process:
1. **Identify the positions at \( t = 10 \) s and \( t = 20 \) s:**
   - From the graph, at \( t = 10 \) s, the position appears to be **20 meters**.
   - At \( t = 20 \) s, the position appears to be **10 meters**.

2. **Calculate the change in position (\( \Delta x \)):**
   \[
   \Delta x = x_2 - x_1 = 10 \, \text{m} - 20 \, \text{m} = -10 \, \text{m}
   \]
   This means the object moved **10 meters backward** during this interval.

3. **Calculate the change in time (\( \Delta t \)):**
   \[
   \Delta t = t_2 - t_1 = 20 \, \text{s} - 10 \, \text{s} = 10 \, \text{s}
   \]

4. **Calculate the average velocity:**
   \[
   v_{\text{avg}} = \frac{-10 \, \text{m}}{10 \, \text{s}} = -1 \, \text{m/s}
   \]
   The average velocity between \( t = 10 \) s and \( t = 20 \) s is **-1 m/s**. The negative sign indicates that the object was moving in the opposite direction (backward).

### Conclusion:
The average velocity from \( t = 10 \) seconds to \( t = 20 \) seconds is **-1 m/s**.

Would you like more details on this, or do you have any questions?

Here are some follow-up questions to expand the topic:
1. What is the significance of a negative velocity?
2. How would you calculate the average speed instead of the average velocity?
3. How can you determine the instantaneous velocity at \( t = 15 \) s from the graph?
4. How would the calculation change if the object had moved in a positive direction?
5. How is displacement different from total distance traveled?

**Tip:** When calculating average velocity, always pay attention to the direction of motion—this is what distinguishes velocity from speed.

find the average velocity from t=10s and t=20s, show all work

Learn how to find the average velocity of an object from t=10s to t=20s using the formula v_avg = Δx / Δt. This problem includes the calculation of displacement and covers essential concepts in kinematics. Suitable for high school students studying motion in physics.

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