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(Figure 1) shows a velocity-versus-time graph for a particle moving along the x-axis. At t = 0 s, assume that x= 0 mm. What is the particle's acceleration at t = 1.0 s?

Express your answer with the appropriate units.

To find the particle's acceleration at \( t = 1.0 \, \text{s} \), we need to first understand the relationship between velocity and acceleration. The acceleration at any given point in time is the slope of the velocity-versus-time graph at that point.

### Steps:
1. **Identify the time period of interest**: The graph shows that between \( t = 0 \, \text{s} \) and \( t = 2 \, \text{s} \), the velocity is constant at \( v_x = 4 \, \text{m/s} \). Constant velocity means the acceleration is zero in this interval.
   
2. **Determine acceleration at \( t = 1.0 \, \text{s} \)**: Since \( t = 1.0 \, \text{s} \) falls within the interval \( 0 \leq t \leq 2 \, \text{s} \), where the velocity is constant, the acceleration is:

\[
a = \frac{\Delta v_x}{\Delta t} = 0 \, \text{m/s}^2
\]

So, the particle's acceleration at \( t = 1.0 \, \text{s} \) is \( 0 \, \text{m/s}^2 \).

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

Here are 5 related questions:
1. What is the acceleration during the interval from \( t = 2 \, \text{s} \) to \( t = 4 \, \text{s} \)?
2. How do you calculate displacement from a velocity vs. time graph?
3. What is the significance of the slope of the graph in terms of motion?
4. How would the graph look for a particle that is accelerating constantly?
5. How does the initial velocity affect the overall motion of a particle?

**Tip**: For motion along a straight line, constant velocity implies zero acceleration, as acceleration represents the rate of change of velocity.

(Figure 1) shows a velocity-versus-time graph for a particle moving along the x-axis. At t = 0 s, assume that x = 0 mm. What is the particle's acceleration at t = 1.0 s? Express your answer with the appropriate units.

Learn how to determine the acceleration of a particle moving along the x-axis from a velocity vs. time graph. This problem covers kinematic concepts such as constant velocity and acceleration. Suitable for Grades 9-12.

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