Motion graph analysis worksheet with distance-time graphs and handwritten answers matching each graph to the correct motion description.

The image you've uploaded is a motion graph analysis worksheet with six distance-time graphs (A–F) and six descriptions of motion. The task is to match each graph to the correct description based on the shape of the graph, which reflects how distance changes over time.

Let’s go through each graph and its corresponding description in detail, explaining why each match is correct.

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🔍 Key Concept: Distance-Time Graphs

In a distance vs. time graph:
- The slope of the line represents speed.
- A flat horizontal line → zero speed (not moving).
- A straight diagonal line → constant speed.
- Steeper slope = higher speed.
- A curved line → changing speed (acceleration or deceleration).
- Curving upward → increasing speed (acceleration).
- Curving downward → decreasing speed (deceleration).

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✔ Graph-by-Graph Analysis:

#### Graph A
- Shape: Horizontal line (constant distance over time)
- Interpretation: No change in distance → object is not moving.
- Matches Description #5: No Motion (stopped)
- Reason: The distance does not change over time → object is at rest.

✔ Correct Match: 5 — *Because the distance is not changing.*

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#### Graph B
- Shape: Straight diagonal line starting from origin, steep slope
- Interpretation: Constant rate of increase in distance → constant high speed.
- Matches Description #2: Constant Speed (high rate of speed)
- Reason: The straight line indicates constant speed; steep slope means high speed.

✔ Correct Match: 2 — *Because the slope of the line is steep.*

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#### Graph C
- Shape: Diagonal line going downward from left to right
- Interpretation: Distance decreases over time → moving back toward the starting point.
- Matches Description #6: Moving Backwards (constant velocity in reverse)
- Reason: Distance is decreasing linearly → constant speed in the reverse direction.

✔ Correct Match: 6 — *Because distance is decreasing as time goes on.*

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#### Graph D
- Shape: Curve that starts flat and becomes steeper (concave up)
- Interpretation: Speed increases over time → accelerating motion.
- Matches Description #1: Acceleration
- Reason: The slope increases over time → speed is increasing.

✔ Correct Match: 1 — *Because the line starts off "slow" and rapidly increases.*

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#### Graph E
- Shape: Curve that starts steep and flattens out (concave down)
- Interpretation: Speed decreases over time → decelerating.
- Matches Description #4: Negative Acceleration (deceleration)
- Reason: The slope decreases over time → slowing down.

✔ Correct Match: 4 — *Because it starts fast and then levels off.*

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#### Graph F
- Shape: Straight diagonal line with a gentle slope
- Interpretation: Constant speed, but lower than Graph B.
- Matches Description #3: Constant Speed (low rate of speed)
- Reason: The slope is constant but not steep → low speed.

✔ Correct Match: 3 — *Because the slope of the line is NOT steep.*

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✔ Final Answers Summary:

| Graph | Description Number | Reason |
|-------|--------------------|--------|
| A | 5 | Distance is not changing → no motion |
| B | 2 | Steep straight line → constant high speed |
| C | 6 | Distance decreasing → moving backwards |
| D | 1 | Slope increases → acceleration |
| E | 4 | Slope decreases → deceleration |
| F | 3 | Gentle slope → constant low speed |

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📝 Notes:

- The handwritten note "'constant' = straight line" is correct: only straight lines represent constant speed.
- Graphs D and E are curved, so they represent changing speed (acceleration/deceleration).
- Graph C shows movement backward because distance is decreasing.

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✔ Conclusion:

All matches in your answer key are correct and well-explained! The reasoning aligns perfectly with the physics of distance-time graphs.

Let me know if you'd like a version of this explained for students or want help creating similar problems!