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The graph you provided displays the velocity \( v_x(t) \) versus time \( t \) for a particle, and the question asks for the particle's acceleration at \( t = 2.0 \, \text{s} \).

### To determine acceleration:
- **Acceleration** is the rate of change of velocity with respect to time, defined as \( a = \frac{\Delta v}{\Delta t} \).
- In this case, the graph shows a linear relationship, meaning that the slope of the velocity-time graph represents the constant acceleration.

### Step-by-step solution:
1. **Identify points from the graph**:
   - At \( t = 0 \, \text{s} \), the velocity \( v_x = 6 \, \text{m/s} \).
   - At \( t = 3 \, \text{s} \), the velocity \( v_x = 0 \, \text{m/s} \).

2. **Calculate the slope of the line (acceleration)**:
   The slope of the line is:
   \[
   a = \frac{\Delta v_x}{\Delta t} = \frac{v_{x2} - v_{x1}}{t_2 - t_1}
   \]
   Using the points \((t_1, v_{x1}) = (0 \, \text{s}, 6 \, \text{m/s})\) and \((t_2, v_{x2}) = (3 \, \text{s}, 0 \, \text{m/s})\):
   \[
   a = \frac{0 \, \text{m/s} - 6 \, \text{m/s}}{3 \, \text{s} - 0 \, \text{s}} = \frac{-6 \, \text{m/s}}{3 \, \text{s}} = -2 \, \text{m/s}^2
   \]

### Result:
The acceleration is constant throughout the time interval, so at \( t = 2.0 \, \text{s} \), the particle's acceleration is:
\[
a = -2 \, \text{m/s}^2
\]

Would you like further details or have any questions? Here are some related questions you could explore:

1. What would be the particle's velocity at \( t = 1 \, \text{s} \)?
2. How far has the particle traveled by \( t = 2.0 \, \text{s} \)?
3. What is the particle's displacement during the entire 3-second interval?
4. What would happen to the motion if the acceleration was positive instead of negative?
5. Can we calculate the average velocity of the particle between \( t = 0 \, \text{s} \) and \( t = 2.0 \, \text{s} \)?

**Tip**: In velocity-time graphs, the slope gives you acceleration, and the area under the curve gives you displacement.

At t = 2.0 s, what is the particle's acceleration? Express your answer with the appropriate units.

Learn how to determine the particle's acceleration at t = 2.0 s using a velocity-time graph. This example covers core kinematic concepts such as the calculation of acceleration from the slope of the graph, suitable for students in Grades 9-12.

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