To find the $x$-component of the object's acceleration, we need to analyze the forces in the horizontal (x) direction, and then apply Newton's second law:

$F = ma$ where:

• $F_x$ is the total force in the $x$-direction.
• $m$ is the mass of the object.
• $a_x$ is the $x$-component of acceleration.

Let's break down the forces in the $x$-direction based on the diagram:

Forces in the $x$-direction:

1. 1.0 N: This force is already along the positive $x$-axis, so it contributes $+1.0 \, \text{N}$.
2. 5.0 N at an angle of 20°: We need the $x$-component of this force. Using the cosine of the angle: $F_{x, 5.0\,N} = 5.0 \cos(20^\circ)$
3. 3.0 N: This force is along the negative $y$-axis and does not have an $x$-component.

Adding these up gives the net force in the $x$-direction: $F_x = 1.0 + 5.0 \cos(20^\circ)$ Once we have the total force, we can calculate the acceleration using $F_x = ma_x$. However, to get the acceleration $a_x$, we also need the mass $m$ of the object, which is not provided in the diagram. If you have the mass, we can continue from there, but if it's not provided, we'll assume it's a known variable.

Let me know if you have the mass or if you'd like to clarify further!

Here are some questions that may help extend this:

1. What is the object's mass?
2. Do you need the $y$-component of the acceleration as well?
3. Should we calculate the net acceleration (magnitude and direction)?
4. Do you need a breakdown of the trigonometric components?
5. Would you like to know how to resolve forces in both axes?

Tip: Always resolve forces along each axis separately and then apply Newton's laws.