Student worksheet on distance-time and velocity-time graphs, with handwritten responses.

It looks like you've uploaded a worksheet titled "Student Exploration: Distance-Time and Velocity-Time Graphs" from the Gizmos platform. The worksheet includes prior knowledge questions, a gizmo warm-up, and instructions for creating graphs using an interactive tool.

However, the image cuts off before showing the full content, particularly the graph that students are supposed to create or analyze. Based on what is visible, I can help you understand and answer the prior knowledge questions and explain the concepts involved. Let's go through them step by step.

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✔ Prior Knowledge Questions

#### 1. Which runner traveled a greater distance?
> Answer: Dora

Explanation:
- Dora runs one complete lap around the track.
- The track is shown as an oval with a straight side of 100 meters. A typical running track is about 400 meters per lap (though not specified here, we infer it’s longer than 100 m).
- Clark runs only 100 meters in a straight line.
- Therefore, Dora travels a greater distance because she runs around the entire loop.

✔ So, Dora is correct.

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#### 2. Which runner had a greater change in position, start to finish?
> Answer: Clark

Explanation:
- Change in position = Displacement (final position – initial position).
- Dora starts and finishes at the same point, so her displacement is zero.
- Clark starts at one end of the straight track and finishes 100 meters ahead — his displacement is 100 meters.
- So, Clark has a greater change in position.

✔ So, Clark is correct.

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🔍 Key Concepts Clarified:

| Term | Definition |
|------|-----------|
| Distance Traveled | Total path length covered (scalar quantity). |
| Displacement | Change in position from start to finish (vector quantity; includes direction). |
| Speed | Rate of change of distance (scalar). |
| Velocity | Rate of change of displacement (vector; includes direction). |

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🧩 Gizmo Warm-Up (Partially Visible)

You're being instructed to:
- Use the Distance-Time and Velocity-Time Graphs Gizmo.
- Set Number of Points = 2.
- Turn on Show graph and Show animation for both runners.
- Drag points to create a specific graph (not visible in your image).

Since the actual graph isn't shown, I can’t guide you on how to drag the points unless you describe or upload the target graph.

But generally:
- In a position-time graph:
- A straight diagonal line means constant velocity.
- A flat horizontal line means the object is at rest.
- The slope of the line = velocity.

For example:
- If Runner 1 moves at constant speed from 0 to 40 meters in 8 seconds → slope = 5 m/s.
- Runner 2 might start later or move faster.

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📌 What You Should Do Next:

If you’re working in the Gizmo:
1. Open the Distance-Time and Velocity-Time Graphs simulation.
2. Follow the instructions to set up two runners.
3. Adjust the points to match the desired motion (e.g., constant speed, starting at different times, etc.).
4. Observe how the velocity-time graph and distance traveled vs. time graphs update.

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❓Need Help With the Graph?

If you can describe or provide:
- The shape of the graph you need to create,
- Or the motion of each runner (e.g., "Runner 1 starts at 0 m and goes to 60 m in 10 s"),
I can help you determine where to place the points.

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✔ Summary of Answers So Far:

| Question | Answer | Reason |
|--------|-------|-------|
| 1. Greater distance? | Dora | She ran a full lap (~400 m), Clark only 100 m |
| 2. Greater change in position? | Clark | Dora ends where she started (displacement = 0); Clark moved 100 m |

Let me know if you'd like help with the graph creation, interpreting velocity-time graphs, or calculating speed/velocity from data!