The image you uploaded shows a system of forces acting on an object. To find the $x$-component of the object's acceleration ($a_x$), we will need to apply Newton's second law, which is:

$F_x = m a_x$

Where:

• $F_x$ is the net force in the $x$-direction.
• $m$ is the mass of the object (which is 2.5 kg).
• $a_x$ is the acceleration in the $x$-direction (which is what we are solving for).

Step 1: Identify the forces in the $x$-direction

From the diagram, we see:

• A force of $4.0 \, \text{N}$ acting to the right (positive $x$-direction).
• A force of $2.0 \, \text{N}$ acting to the left (negative $x$-direction).

Step 2: Calculate the net force in the $x$-direction

The net force in the $x$-direction ($F_x$) is the sum of all forces acting along the $x$-axis:

$F_x = 4.0 \, \text{N} - 2.0 \, \text{N} = 2.0 \, \text{N}$

Step 3: Apply Newton's second law

Using $F_x = m a_x$, we can now solve for $a_x$:

$2.0 \, \text{N} = 2.5 \, \text{kg} \cdot a_x$

$a_x = \frac{2.0 \, \text{N}}{2.5 \, \text{kg}} = 0.8 \, \text{m/s}^2$

Conclusion:

The $x$-component of the object's acceleration is $a_x = 0.8 \, \text{m/s}^2$.

Would you like further details or explanations on this?

Here are 5 related questions to consider:

1. What is the $y$-component of the object's acceleration?
2. How do the forces in the $y$-direction affect the overall motion?
3. Can the net force and acceleration be represented as vectors?
4. How would the motion change if the mass of the object were doubled?
5. What would happen to the acceleration if an additional force were applied along the $x$-axis?

Tip: When working with forces, always separate components along different axes to simplify your calculations.