https://file.aiquickdraw.com/mathbot/file/17289705234143amfp8ao.jpg

Let's analyze each graph in the context of physics:

### **Position vs. Time Graphs (F, G, H):**
1. **Graph F:** A linearly increasing position suggests constant positive velocity.
2. **Graph G:** A horizontal line indicates the object is stationary (velocity = 0).
3. **Graph H:** A decreasing position suggests negative velocity (moving backward).

### **Velocity vs. Time Graphs (P, Q, R):**
1. **Graph P:** Constant positive slope, which indicates constant positive acceleration.
2. **Graph Q:** Zero slope (horizontal line) shows constant velocity.
3. **Graph R:** Constant negative velocity (straight line below the time axis) suggests the object is moving backward at a constant speed.

### **Acceleration vs. Time Graphs (S, T, U):**
1. **Graph S:** Positive constant acceleration (above the time axis).
2. **Graph T:** Zero acceleration indicates no change in velocity.
3. **Graph U:** Negative constant acceleration (below the time axis).

### **Matching:**
- **F (constant positive velocity)** should match with **Q (constant velocity)** and **T (zero acceleration)**.
- **G (stationary object)** should match with **Q (constant zero velocity)** and **T (zero acceleration)**.
- **H (negative velocity)** should match with **R (negative constant velocity)** and **U (negative constant acceleration)**.

### Best Answer: **d) H, Q, and U**

Would you like a detailed explanation of any part of this? 

Here are some follow-up questions for deeper understanding:
1. What is the physical meaning of the slope in a position vs. time graph?
2. How can you tell if an object is accelerating from a velocity vs. time graph?
3. Why is acceleration constant in graph S but zero in graph T?
4. How does the sign of acceleration relate to the direction of motion?
5. What would an object with zero velocity and nonzero acceleration look like on these graphs?

**Tip:** In physics, the slope of the position vs. time graph always gives the velocity, and the slope of the velocity vs. time graph gives the acceleration.

The illustration shows three rows of graphs: The top row shows three position versus time graphs, the middle row shows three velocity versus time graphs, and the bottom row shows three acceleration versus time graphs. Which graphs—one from each row—are the best match?

Explore how to match position, velocity, and acceleration graphs based on their physical meanings in kinematics. Learn how to interpret constant velocity, zero acceleration, and negative velocity through graphical analysis. Suitable for high school students in Grades 9-12.

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