Position-Time Graph and Velocity-Time Graph Review by Liz Nisbet STEM - Free Printable

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 guide you through how to solve typical problems related to position-time and velocity-time graphs, based on the structure of your worksheet.

Let’s assume a common scenario for such a problem (as it appears from your text):

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Assumed Position-Time Graph Description:

Let’s suppose the position-time graph shows the following:

- The object starts at position 0 m at time 0 s.
- From 0 to 2 seconds: moves with constant positive velocity (straight line upward).
- From 2 to 5 seconds: continues moving forward but at a slower rate (less steep slope).
- From 5 to 7 seconds: stops (horizontal line).
- From 7 to 10 seconds: moves backward (negative direction), returning to the origin at t = 12 seconds.

This is a typical motion pattern used in these types of problems.

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Now, let's go through each question step by step.

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1. Describe the motion of the object from:

#### a) 0–2 seconds
- The graph shows a straight line with a positive slope.
- This means the object is moving in the positive direction with constant velocity.
- Motion: Constant speed in the positive direction.

#### b) 2–5 seconds
- Still a straight line, but less steep than before.
- Slope is still positive but smaller → slower constant velocity in the positive direction.
- Motion: Moving forward, but slowing down? No — wait: if slope is constant, velocity is constant. So it's just moving forward at a lower constant speed.

> Note: "Slowing down" implies changing velocity (acceleration). But since the graph is linear, velocity is constant.

So: Constant velocity in the positive direction, but less than before.

#### c) 5–7 seconds
- Horizontal line → slope = 0 → velocity = 0.
- Object is at rest.

#### d) 9–12 seconds
- Line goes downward → negative slope → moving in the negative direction.
- If it's a straight line, velocity is constant and negative.
- So: Moving backward at constant speed.

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2. What is the total distance traveled?

- Distance is the total path length (scalar quantity).
- We need to calculate the sum of all segments:
- From 0 to 2 s: say it goes from 0 to 6 m → 6 m
- From 2 to 5 s: from 6 m to 10 m → 4 m
- From 5 to 7 s: stays at 10 m → 0 m
- From 7 to 12 s: goes from 10 m back to 0 m → 10 m

Total distance = 6 + 4 + 0 + 10 = 20 meters

> ✔ Answer: 20 meters

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3. What is the total displacement of the object?

- Displacement = final position – initial position
- Starts at 0 m, ends at 0 m (back at origin)
- So: 0 meters

> ✔ Answer: 0 meters

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4. What is the average velocity of the object?

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

Average velocity = 0 / 12 = 0 m/s

> ✔ Answer: 0 m/s

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5. What is the average speed of the object?

- Average speed = total distance / total time
- Distance = 20 m
- Time = 12 s

Average speed = 20 / 12 ≈ 1.67 m/s

> ✔ Answer: 1.67 m/s

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

We need to determine the slope of the position-time graph in each segment:

| Time Interval | Slope (Velocity) | Velocity |
|---------------|------------------|----------|
| 0–2 s | Rise = 6 m, Run = 2 s → 3 m/s | +3 m/s |
| 2–5 s | Rise = 4 m, Run = 3 s → 1.33 m/s | +1.33 m/s |
| 5–7 s | Flat → slope = 0 | 0 m/s |
| 7–12 s | Fall from 10 m to 0 m over 5 s → -2 m/s | -2 m/s |

Now draw the velocity-time graph:

- From 0 to 2 s: horizontal line at +3 m/s
- From 2 to 5 s: horizontal line at +1.33 m/s
- From 5 to 7 s: horizontal line at 0 m/s
- From 7 to 12 s: horizontal line at -2 m/s

> ✔ Plot these as horizontal lines on a velocity-time graph.

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Summary of Answers:

1. Motion descriptions:
- a) Constant positive velocity
- b) Constant positive velocity (but slower)
- c) At rest
- d) Constant negative velocity

2. Total distance: 20 m
3. Displacement: 0 m
4. Average velocity: 0 m/s
5. Average speed: 1.67 m/s
6. Velocity-time graph: piecewise horizontal lines at +3, +1.33, 0, and -2 m/s

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⚠️ Note: These answers are based on an assumed graph. If your actual graph differs (e.g., different slopes, times, or shapes), please describe it (or provide coordinates), and I can adjust the solution accordingly.

Would you like me to help you sketch the velocity-time graph or explain any part in more detail?