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.