Worksheet on position, distance, and displacement with a diagram of a dog's movement on a number line.

Problem Analysis:

The task involves understanding the concepts of position, displacement, and distance based on a number line. Let's break down each question step by step.

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#### Question 1: What is the correct description of any change of position farther to the right of zero?
- Options:
- a) negative displacement
- b) positive distance
- c) negative distance
- d) positive change of displacement

Explanation:
- Position: The location of an object on the number line.
- Displacement: The change in position, which includes both magnitude and direction.
- Distance: The total length traveled, regardless of direction.

When an object moves farther to the right of zero, it means the object is moving in the positive direction on the number line. This corresponds to a positive displacement because displacement accounts for direction (rightward movement is positive).

Answer:
$$
\boxed{d}
$$

---

#### Question 2: A dog adds from -6 m to +2 m. Which of the following statements is true about the dog’s motion?
- Options:
- A. Δx = -3 + 2 (-1 m)
- B. Δx = -6 + 2 (-4 m)
- C. Δx = -6 + 2 (+2 m)
- D. Δx = -6 + 2 (+8 m)

Explanation:
- Displacement (Δx) is calculated as the final position minus the initial position:
$$
\Delta x = x_{\text{final}} - x_{\text{initial}}
$$
- Here, the initial position ($x_{\text{initial}}$) is $-6 \, \text{m}$, and the final position ($x_{\text{final}}$) is $+2 \, \text{m}$.
- Therefore:
$$
\Delta x = 2 - (-6) = 2 + 6 = 8 \, \text{m}
$$

Answer:
$$
\boxed{D}
$$

---

#### Question 3: What is the maximum negative displacement a dog could have if it started at position 0?
- Options:
- A. -7 m
- B. -9 m
- C. -10 m
- D. -70 m

Explanation:
- Displacement is the change in position relative to the starting point.
- If the dog starts at position $0$, the maximum negative displacement occurs when the dog moves as far left as possible on the number line.
- From the given options, the most negative value is $-70 \, \text{m}$.

Answer:
$$
\boxed{D}
$$

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#### Questions 4–9: Use the number line below to answer the following questions.

The number line is not explicitly provided in the text, but we can infer its structure based on typical problems of this type. Assume the number line ranges from $-10$ to $+10$ with marked points $A$, $B$, $C$, and $D$.

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#### Question 4: What is the object’s displacement if it travels from point $D$ to $C$?
- Assumption:
- Point $D$ is at $+10 \, \text{m}$.
- Point $C$ is at $+5 \, \text{m}$.

Calculation:
- Displacement ($\Delta x$) is:
$$
\Delta x = x_{\text{final}} - x_{\text{initial}} = 5 - 10 = -5 \, \text{m}
$$

Answer:
$$
\boxed{-5 \, \text{m}}
$$

---

#### Question 5: What distance does the object travel if it moves from point $D$ to $B$?
- Assumption:
- Point $D$ is at $+10 \, \text{m}$.
- Point $B$ is at $-5 \, \text{m}$.

Calculation:
- Distance is the total length traveled, regardless of direction:
$$
\text{Distance} = |x_{\text{final}} - x_{\text{initial}}| = |(-5) - 10| = |-15| = 15 \, \text{m}
$$

Answer:
$$
\boxed{15 \, \text{m}}
$$

---

#### Question 6: What is the object’s displacement if it moves from point $B$ to $C$?
- Assumption:
- Point $B$ is at $-5 \, \text{m}$.
- Point $C$ is at $+5 \, \text{m}$.

Calculation:
- Displacement ($\Delta x$) is:
$$
\Delta x = x_{\text{final}} - x_{\text{initial}} = 5 - (-5) = 5 + 5 = 10 \, \text{m}
$$

Answer:
$$
\boxed{10 \, \text{m}}
$$

---

#### Question 7: What is the distance the object travels if it moves from point $A$ to $B$ and then back to $C$?
- Assumption:
- Point $A$ is at $-10 \, \text{m}$.
- Point $B$ is at $-5 \, \text{m}$.
- Point $C$ is at $+5 \, \text{m}$.

Calculation:
1. Distance from $A$ to $B$:
$$
\text{Distance}_{AB} = |x_B - x_A| = |-5 - (-10)| = |-5 + 10| = 5 \, \text{m}
$$
2. Distance from $B$ to $C$:
$$
\text{Distance}_{BC} = |x_C - x_B| = |5 - (-5)| = |5 + 5| = 10 \, \text{m}
$$
3. Total distance:
$$
\text{Total Distance} = \text{Distance}_{AB} + \text{Distance}_{BC} = 5 + 10 = 15 \, \text{m}
$$

Answer:
$$
\boxed{15 \, \text{m}}
$$

---

#### Question 8: What is the object’s displacement if it moves from point $D$ to $C$ to $A$ to $B$?
- Assumption:
- Point $D$ is at $+10 \, \text{m}$.
- Point $C$ is at $+5 \, \text{m}$.
- Point $A$ is at $-10 \, \text{m}$.
- Point $B$ is at $-5 \, \text{m}$.

Calculation:
1. Displacement from $D$ to $C$:
$$
\Delta x_{DC} = x_C - x_D = 5 - 10 = -5 \, \text{m}
$$
2. Displacement from $C$ to $A$:
$$
\Delta x_{CA} = x_A - x_C = -10 - 5 = -15 \, \text{m}
$$
3. Displacement from $A$ to $B$:
$$
\Delta x_{AB} = x_B - x_A = -5 - (-10) = -5 + 10 = 5 \, \text{m}
$$
4. Total displacement:
$$
\Delta x_{\text{total}} = \Delta x_{DC} + \Delta x_{CA} + \Delta x_{AB} = -5 + (-15) + 5 = -15 \, \text{m}
$$

Answer:
$$
\boxed{-15 \, \text{m}}
$$

---

#### Question 9: What distance does the object travel if it moves from point $D$ to $C$ to $A$ to $B$?
- Assumption:
- Point $D$ is at $+10 \, \text{m}$.
- Point $C$ is at $+5 \, \text{m}$.
- Point $A$ is at $-10 \, \text{m}$.
- Point $B$ is at $-5 \, \text{m}$.

Calculation:
1. Distance from $D$ to $C$:
$$
\text{Distance}_{DC} = |x_C - x_D| = |5 - 10| = 5 \, \text{m}
$$
2. Distance from $C$ to $A$:
$$
\text{Distance}_{CA} = |x_A - x_C| = |-10 - 5| = 15 \, \text{m}
$$
3. Distance from $A$ to $B$:
$$
\text{Distance}_{AB} = |x_B - x_A| = |-5 - (-10)| = |-5 + 10| = 5 \, \text{m}
$$
4. Total distance:
$$
\text{Total Distance} = \text{Distance}_{DC} + \text{Distance}_{CA} + \text{Distance}_{AB} = 5 + 15 + 5 = 25 \, \text{m}
$$

Answer:
$$
\boxed{25 \, \text{m}}
$$

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Final Answers:

1. $\boxed{d}$
2. $\boxed{D}$
3. $\boxed{D}$
4. $\boxed{-5 \, \text{m}}$
5. $\boxed{15 \, \text{m}}$
6. $\boxed{10 \, \text{m}}$
7. $\boxed{15 \, \text{m}}$
8. $\boxed{-15 \, \text{m}}$
9. $\boxed{25 \, \text{m}}$