An object at (4, 9) moves in straight-line two-dimensional motion to a position of (-4, 3). After that, it has a displacement of 0 m in the negative yy-direction. Immediately after that, it moves in straight-line two-dimensional motion to a final position of (4, 3). Determine the distance traveled by the object going from its initial position to its final position. Express your answer rounded to 3 significant figures.

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.

Learn how to calculate the distance traveled by an object in two-dimensional motion. Solve a problem involving straight-line motion and displacement using the distance formula. Suitable for Grades 9-12.

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