To determine the distance traveled by the object, we'll break down its motion into segments and calculate the distance for each segment before summing them up.

Step 1: Calculate the distance between the initial position $(4, 9)$ and the position $(-4, 3)$

We use the distance formula:

$\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

For the points $(4, 9)$ and $(-4, 3)$:

$\text{Distance}_1 = \sqrt{(-4 - 4)^2 + (3 - 9)^2} = \sqrt{(-8)^2 + (-6)^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \, \text{m}$

Step 2: Consider the displacement in the negative $y$-direction

The problem states the object has a displacement of 0 m in the negative $y$-direction, so this segment doesn't contribute to the total distance:

$\text{Distance}_2 = 0 \, \text{m}$

Step 3: Calculate the distance between the position $(-4, 3)$ and the final position $(4, 3)$

Using the points $(-4, 3)$ and $(4, 3)$:

$\text{Distance}_3 = \sqrt{(4 - (-4))^2 + (3 - 3)^2} = \sqrt{(4 + 4)^2 + 0^2} = \sqrt{8^2} = \sqrt{64} = 8 \, \text{m}$

Step 4: Sum the distances to find the total distance traveled

Add up the distances from each segment:

$\text{Total Distance} = \text{Distance}_1 + \text{Distance}_2 + \text{Distance}_3 = 10 + 0 + 8 = 18 \, \text{m}$

So, the total distance traveled by the object is 18.0 meters.

Would you like further details or have any questions?

Here are some related questions:

1. What would be the total displacement for this motion?
2. How would the total distance change if the object had a non-zero displacement in the negative $y$-direction?
3. How does the concept of distance differ from displacement in physics?
4. What if the object moved along a curved path instead of a straight line? How would that affect the distance?
5. Can the distance traveled ever be less than the magnitude of the displacement?

Tip: Remember, distance traveled depends on the path taken, while displacement is only concerned with the initial and final positions.