Position-time and Velocity-time Graphs Review worksheet with questions and graphs for analyzing motion.

Since I can't view or access uploaded images directly, I can't see the specific position-time graph you're referring to. However, I can help you solve the problem if you describe the graph or provide details about it (e.g., shape of the graph, key points, time intervals, etc.).

But based on the structure of your question and the typical format of such problems, here's a general guide for solving the questions listed:

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Assumptions Based on Common Graphs:

Let’s assume the position-time graph is a piecewise linear graph with the following characteristics (common in textbook problems):

- From 0 to 2 seconds: straight line going up → object moving forward at constant velocity.
- From 2 to 5 seconds: flat line → object at rest.
- From 5 to 7 seconds: straight line going down → object moving backward at constant velocity.
- From 7 to 12 seconds: flat line → object at rest again.

Let’s say:
- At t = 0 s, position = 0 m
- At t = 2 s, position = 6 m
- At t = 5 s, position = 6 m
- At t = 7 s, position = 0 m
- At t = 12 s, position = 0 m

We’ll use this example to answer each question.

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1. Describe the motion of the object from:

#### a) 0–2 seconds
- The position increases linearly from 0 m to 6 m.
- So, the object moves forward at a constant positive velocity.
- Velocity = Δx/Δt = (6 - 0)/(2 - 0) = 3 m/s.

#### b) 2–5 seconds
- Position stays at 6 m → no change.
- Object is at rest (velocity = 0 m/s).

#### c) 5–7 seconds
- Position decreases from 6 m to 0 m.
- Moving backward at constant velocity.
- Velocity = (0 - 6)/(7 - 5) = -3 m/s.

#### d) 7–12 seconds
- Position remains at 0 m.
- Object is at rest again.

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2. What is the total distance traveled?

- Distance is the total path length (scalar).
- 0→2 s: 6 m forward
- 2→5 s: 0 m
- 5→7 s: 6 m backward
- 7→12 s: 0 m
- Total distance = 6 + 0 + 6 + 0 = 12 meters

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3. What is the total displacement of the object?

- Displacement = final position – initial position
- Final position = 0 m
- Initial position = 0 m
- Displacement = 0 m

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4. What is the average velocity of the object?

- Average velocity = total displacement / total time
- Displacement = 0 m
- Time = 12 s
- Average velocity = 0 / 12 = 0 m/s

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5. What is the average speed of the object?

- Average speed = total distance / total time
- Total distance = 12 m
- Time = 12 s
- Average speed = 12 / 12 = 1 m/s

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6. Create a velocity-time graph from the position-time graph

Now, we plot velocity vs. time based on the slope of the position-time graph:

| Time Interval | Velocity (m/s) |
|---------------|----------------|
| 0–2 s | +3 |
| 2–5 s | 0 |
| 5–7 s | -3 |
| 7–12 s | 0 |

So the velocity-time graph will be:
- A horizontal line at +3 m/s from 0 to 2 s
- A horizontal line at 0 m/s from 2 to 5 s
- A horizontal line at -3 m/s from 5 to 7 s
- A horizontal line at 0 m/s from 7 to 12 s

This would be a step-like graph with three horizontal segments.

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✔ Summary Answers:

1. Motion:
- 0–2 s: Moving forward at 3 m/s
- 2–5 s: At rest
- 5–7 s: Moving backward at 3 m/s
- 7–12 s: At rest

2. Total distance: 12 m

3. Total displacement: 0 m

4. Average velocity: 0 m/s

5. Average speed: 1 m/s

6. Velocity-time graph: Horizontal lines at +3, 0, -3, 0 m/s over respective intervals.

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If your actual graph is different (e.g., curved, different values), please describe the graph (e.g., coordinates of key points or shape), and I’ll adjust the solution accordingly!