Worksheet for analyzing distance vs. time graphs, including matching, interpreting, and sketching exercises.

Let's solve this step-by-step based on the distance vs. time graph and the instructions provided.

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Part 1: Match each description to a segment of the graph (Questions 1–5)

We are given a distance vs. time graph with labeled segments: A, B, C, D, E.

- Distance is on the y-axis.
- Time is on the x-axis.

#### Key Concepts:
- Flat line (horizontal) → Distance is not changing → Object is still.
- Straight diagonal line upward → Moving away at constant speed.
- Straight diagonal line downward → Moving closer at constant speed.
- Curved upward (increasing slope) → Moving away at increasing speed.
- Curved downward (decreasing slope) → Moving closer and slowing down.

Now let’s analyze each segment:

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#### Segment A:
- Starts at origin, goes up with constant positive slope.
- So, moving away at constant speed.

✔ Match to #2

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#### Segment B:
- Still going up, but steeper than A.
- The slope increases → accelerating, moving away faster.
- So, moving away at increasing speed.

✔ Match to #4

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#### Segment C:
- Horizontal line → distance is constant.
- So, object is still.

✔ Match to #1

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#### Segment D:
- Going downward, straight line → decreasing distance at constant rate.
- So, moving closer at constant speed.

✔ Match to #3

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#### Segment E:
- Going downward, but the curve is flattening out (slope decreasing).
- This means it's slowing down while getting closer.
- So, moving closer and decreasing its speed.

✔ Match to #5

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✔ Answers for 1–5:

1. C
2. A
3. D
4. B
5. E

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Part 2: Interpret each part of the graph as Grant’s hike (Questions 6–10)

Assume the graph represents Grant’s distance from the base of a hiking trail.

So:
- Increasing distance = moving away from base (up the trail).
- Decreasing distance = moving toward base.
- Flat = stopped.

Let’s interpret each segment:

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#### 6. A
- Distance increases steadily → Grant is walking away from the base at a constant speed.
- ➤ Grant starts hiking up the trail at a constant speed.

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#### 7. B
- Slope increases → he's accelerating (speeding up).
- ➤ Grant speeds up while hiking further up the trail.

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#### 8. C
- Horizontal line → distance stays the same → he stops.
- ➤ Grant stops hiking (resting or taking a break).

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#### 9. D
- Distance decreases steadily → he’s returning toward the base.
- Constant slope → constant speed.
- ➤ Grant walks back down the trail at a constant speed.

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#### 10. E
- Curve going down, flattening → slowing down while returning.
- ➤ Grant slows down as he approaches the base of the trail.

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✔ Answers for 6–10:

6. Grant hikes away from the base at a constant speed.
7. Grant hikes away from the base at an increasing speed.
8. Grant stops hiking (rests).
9. Grant hikes back toward the base at a constant speed.
10. Grant hikes back toward the base and slows down.

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Part 3: Sketch Tyra’s distance vs. time graph (Question 11)

We are to sketch a distance vs. time graph based on her movements.

Let’s go through each event:

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#### A. Tyra left science class to use the restroom.
- She moves away from class → distance increases.
- Let’s assume she walks at a steady pace → straight upward line.

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#### B. Halfway there, she realized she forgot the hall pass and went back to get it.
- She was halfway → distance is half the max.
- Then turns around → distance decreases back to zero (back to class).
- So, from point A, she goes up to midpoint, then back down to 0.
- This creates a V-shaped dip.

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#### C. Tyra walked to the restroom with the pass.
- Now she leaves again → distance increases again.
- But this time, she doesn’t stop — goes all the way to restroom.
- So, line goes up again, possibly same speed.

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#### D. Tyra used the restroom and washed her hands.
- She’s at the restroom → distance stays constant.
- So, horizontal line (flat).

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#### E. Tyra remembered her teacher told her to hurry, so she quickly walked back to class.
- She returns → distance decreases.
- But now she’s walking quickly → steeper downward slope.

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✔ Graph Description (Sketch Instructions):

1. Start at origin (class).
2. Segment A: Line goes up at moderate slope → to halfway point.
3. Segment B: Line goes back down to zero (returns to class) → same slope (same speed).
4. Segment C: Line goes up again (leaves class with pass) → to full distance (restroom).
5. Segment D: Horizontal line → stays at restroom (using it).
6. Segment E: Steep downward line → returns quickly to class.

> Note: Since we can't draw here, you’d label the segments:
> - A: Up to halfway
> - B: Down to class
> - C: Up to restroom
> - D: Flat at restroom
> - E: Steep down to class

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✔ Final Answer Summary:

#### 1–5 Matching:
1. C
2. A
3. D
4. B
5. E

#### 6–10 Interpretations:
6. Grant hikes away from the base at a constant speed.
7. Grant hikes away from the base at an increasing speed.
8. Grant stops hiking (rests).
9. Grant hikes back toward the base at a constant speed.
10. Grant hikes back toward the base and slows down.

#### 11. Tyra’s Graph:
- A: Rising line to halfway point.
- B: Falling line back to zero (class).
- C: Rising line to full distance (restroom).
- D: Horizontal line (stopped at restroom).
- E: Steep falling line back to zero (quick return).

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This completes the entire worksheet! Let me know if you'd like a visual sketch description or printable version.