Physics worksheet on distance and displacement with illustrated scenarios of movement from a house to different destinations.

Problem Analysis:

The worksheet asks us to calculate the distance and displacement for three different scenarios involving Lucinda's movements. Let's solve each problem step by step.

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Definitions Recap:

1. Distance: The total path length traveled, regardless of direction. It is a scalar quantity.
2. Displacement: The straight-line distance between the starting point and the ending point, along with its direction. It is a vector quantity.

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Problem #1:

Scenario: Lucinda walked 400 m west from her house to the school.

#### Step 1: Distance
- Distance is the total path length traveled.
- Lucinda walked 400 m directly.
- Therefore, the distance is:
\[
\text{Distance} = 400 \, \text{m}
\]

#### Step 2: Displacement
- Displacement is the straight-line distance from the starting point (house) to the ending point (school).
- Lucinda moved 400 m west.
- Therefore, the displacement is:
\[
\text{Displacement} = 400 \, \text{m west}
\]

#### Final Answer for Problem #1:
\[
\boxed{\text{Distance} = 400 \, \text{m}, \, \text{Displacement} = 400 \, \text{m west}}
\]

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Problem #2:

Scenario: Lucinda walked 300 m east to the street corner. She then walked another 600 m east to the park.

#### Step 1: Distance
- Distance is the total path length traveled.
- Lucinda walked 300 m + 600 m = 900 m.
- Therefore, the distance is:
\[
\text{Distance} = 900 \, \text{m}
\]

#### Step 2: Displacement
- Displacement is the straight-line distance from the starting point (house) to the ending point (park).
- Lucinda moved 300 m east initially and then an additional 600 m east.
- Total displacement in the east direction:
\[
\text{Displacement} = 300 \, \text{m} + 600 \, \text{m} = 900 \, \text{m east}
\]

#### Final Answer for Problem #2:
\[
\boxed{\text{Distance} = 900 \, \text{m}, \, \text{Displacement} = 900 \, \text{m east}}
\]

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Problem #3:

Scenario: Lucinda walked 400 m west from her house to the school. She then turned and walked 400 m east back to her house.

#### Step 1: Distance
- Distance is the total path length traveled.
- Lucinda walked 400 m west and then 400 m east.
- Total distance:
\[
\text{Distance} = 400 \, \text{m} + 400 \, \text{m} = 800 \, \text{m}
\]

#### Step 2: Displacement
- Displacement is the straight-line distance from the starting point (house) to the ending point (house).
- Lucinda started at the house, walked 400 m west, and then returned 400 m east.
- Since she ended up at the same point where she started, her net displacement is:
\[
\text{Displacement} = 0 \, \text{m}
\]

#### Final Answer for Problem #3:
\[
\boxed{\text{Distance} = 800 \, \text{m}, \, \text{Displacement} = 0 \, \text{m}}
\]

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Summary of Answers:

1. \(\boxed{\text{Distance} = 400 \, \text{m}, \, \text{Displacement} = 400 \, \text{m west}}\)
2. \(\boxed{\text{Distance} = 900 \, \text{m}, \, \text{Displacement} = 900 \, \text{m east}}\)
3. \(\boxed{\text{Distance} = 800 \, \text{m}, \, \text{Displacement} = 0 \, \text{m}}\)