We are given the following information:

• Mass of the particle: $m = 2 \, \text{kg}$
• Velocity function: $v(t) = 3t - 4 \, \text{m/s}$
• Force function: $F(t) = -k \cdot v(t)$ where $k = 5 \, \text{N} \cdot \text{s/m}$
• Time of interest: $t = 2 \, \text{s}$

Step 1: Calculate the velocity at $t = 2 \, \text{s}$

To find the velocity of the particle at $t = 2 \, \text{s}$, we substitute $t = 2$ into the velocity equation:

$v(2) = 3(2) - 4 = 6 - 4 = 2 \, \text{m/s}$

Step 2: Calculate the force at $t = 2 \, \text{s}$

Next, use the force equation $F(t) = -k \cdot v(t)$ to find the force at $t = 2$:

$F(2) = -5 \cdot v(2) = -5 \cdot 2 = -10 \, \text{N}$

Step 3: Use Newton's Second Law to find the acceleration

Newton's second law relates force and acceleration as:

$F = m \cdot a$

Solving for acceleration:

$a = \frac{F}{m} = \frac{-10}{2} = -5 \, \text{m/s}^2$

Final Answer:

The acceleration of the particle at $t = 2 \, \text{s}$ is $\boxed{-5 \, \text{m/s}^2}$.

Do you want more details, or do you have any other questions?

Here are 5 related questions:

1. How would the acceleration change if the mass were doubled?
2. What is the velocity of the particle at $t = 3 \, \text{s}$?
3. How would the force change if $k$ were reduced to 3 N·s/m?
4. Can the particle come to rest? If so, when?
5. How does the velocity vary over time? Can you graph it?

Tip: The force $F(t) = -k \cdot v(t)$ is a damping force, which reduces the velocity of the particle over time.