https://file.aiquickdraw.com/mathbot/file/1727054990857n1q0evaw.jpg

Let's analyze the image and break down the problem step by step.

Path **C** (shown in red) involves motion on the displacement axis (x-axis). From the figure:
- Path **C** starts at \(x = 4 \, \text{m}\),
- It travels to \(x = 10 \, \text{m}\),
- Then it turns back to \(x = 7 \, \text{m}\).

We can now address the questions:

### (a) **The distance traveled (in m):**
- Distance is the total path length covered, regardless of direction.
1. From \(x = 4 \, \text{m}\) to \(x = 10 \, \text{m}\) (forward) → \(10 - 4 = 6 \, \text{m}\),
2. From \(x = 10 \, \text{m}\) back to \(x = 7 \, \text{m}\) (backward) → \(10 - 7 = 3 \, \text{m}\).

So, total distance = \(6 \, \text{m} + 3 \, \text{m} = 9 \, \text{m}\).

### (b) **The magnitude of the displacement (in m) from start to finish:**
- Displacement is the shortest straight-line distance between the starting and ending points.
- Path **C** starts at \(x = 4 \, \text{m}\) and ends at \(x = 7 \, \text{m}\).

So, displacement = \(7 - 4 = 3 \, \text{m}\).

### (c) **The displacement (in m) from start to finish:**
- Displacement includes the direction. Since the movement is to the right (positive x-direction), the displacement is:
  - \(+3 \, \text{m}\).

### Summary:
- (a) Distance traveled = \(9 \, \text{m}\),
- (b) Magnitude of displacement = \(3 \, \text{m}\),
- (c) Displacement = \(+3 \, \text{m}\).

Would you like more details on any step? Let me know if you have any questions!

Here are 5 related questions:
1. What is the difference between distance and displacement?
2. How does reversing direction affect the total distance but not the displacement?
3. Can displacement ever be larger than the total distance?
4. How is velocity related to displacement?
5. What is the significance of the positive and negative signs in displacement?

**Tip:** In physics, **distance** is a scalar quantity (only magnitude), while **displacement** is a vector (magnitude and direction).

Find the following for path C in the figure below:
(a) the distance traveled (in m)
(b) the magnitude of the displacement (in m) from start to finish
(c) the displacement (in m) from start to finish

Learn how to calculate the total distance traveled and the displacement for Path C in a motion diagram. This problem covers key physics concepts of displacement and distance. Suitable for students in Grades 9-12.

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