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To calculate the average acceleration (\( a_{av,x} \)) between \( t = 7.00 \, \text{s} \) and \( t = 11.0 \, \text{s} \), we use the formula for average acceleration:

\[
a_{av,x} = \frac{\Delta v_x}{\Delta t}
\]

Where:
- \( \Delta v_x \) is the change in velocity in the x-direction.
- \( \Delta t \) is the change in time.

### Step 1: Find \( v_x \) at \( t = 7.00 \, \text{s} \)
From the graph, at \( t = 7.00 \, \text{s} \), the velocity \( v_x \) is 5 m/s.

### Step 2: Find \( v_x \) at \( t = 11.0 \, \text{s} \)
At \( t = 11.0 \, \text{s} \), the velocity \( v_x \) is 15 m/s.

### Step 3: Calculate \( \Delta v_x \)
\[
\Delta v_x = v_x(11.0 \, \text{s}) - v_x(7.00 \, \text{s}) = 15 \, \text{m/s} - 5 \, \text{m/s} = 10 \, \text{m/s}
\]

### Step 4: Calculate \( \Delta t \)
\[
\Delta t = 11.0 \, \text{s} - 7.00 \, \text{s} = 4.00 \, \text{s}
\]

### Step 5: Calculate \( a_{av,x} \)
\[
a_{av,x} = \frac{10 \, \text{m/s}}{4.00 \, \text{s}} = 2.5 \, \text{m/s}^2
\]

Thus, the average acceleration \( a_{av,x} \) between \( t = 7.00 \, \text{s} \) and \( t = 11.0 \, \text{s} \) is \( 2.5 \, \text{m/s}^2 \).

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Do you have any questions or would you like further details on any part of the solution?

Here are five related questions to extend your understanding:
1. How would you calculate the average velocity in the same time interval?
2. What is the significance of the slope of the \( v_x(t) \) graph?
3. How would you determine the total distance traveled between \( t = 7.00 \, \text{s} \) and \( t = 11.0 \, \text{s} \)?
4. What would the graph of acceleration versus time look like based on this velocity graph?
5. How does constant velocity relate to zero acceleration?

**Tip**: The area under the velocity-time graph gives the displacement over a time interval.

What is a_av,x between t = 7.00 s and t = 11.0 s for a car traveling in a straight line as shown in the vx(t) graph?

Learn how to calculate the average acceleration (a_av,x) of a car between t = 7.00 s and t = 11.0 s using a velocity-time graph. This problem involves basic kinematics and is suitable for high school students in Grades 9-12.

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