This physics worksheet guides students through analyzing a position-time graph to determine a car's speed, direction, and stops over a 14-hour period.

Thank you for uploading the image. I’ll solve each question step-by-step based on the position-time graph provided. The graph plots position (in kilometers) on the vertical axis vs. time (in hours) on the horizontal axis.

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Key Concepts:

- Slope of position-time graph = velocity
- Positive slope → moving away from detector (+x direction)
- Negative slope → moving toward detector (-x direction)
- Zero slope → stationary
- Average velocity = change in position / change in time = Δx / Δt
- Distance traveled is total path length; displacement is final position minus initial position.
- Speed limit: 10 km/hr — we’ll find where |velocity| > 10 km/hr.

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Let’s label key points from the graph:

| Point | Time (h) | Position (km) |
|-------|----------|---------------|
| O | 0 | 0 |
| A | 2 | 24 |
| B | 5 | 24 |
| C | 7 | 16 |
| D | 9 | 16 |
| E | 10 | 8 |
| F | 11 | 8 |
| G | 15 | 24 |

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## ✔ Question 1: What is the car doing from “O” to “A” and from “F” to “G”?

- O to A: Position increases from 0 km to 24 km in 2 hours → moving away from detector at constant speed.
- F to G: Position increases from 8 km to 24 km in 4 hours (from t=11 to t=15) → moving away from detector at constant speed.

> Answer: From O to A, the car is moving away from the detector. From F to G, the car is also moving away from the detector.

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## ✔ Question 2: What is happening between “A” to “B”, “C” to “D”, and “E” to “F”?

Look at the slope — if it’s flat (horizontal), the object is stationary.

- A to B (t=2 to t=5): position stays at 24 km → stopped
- C to D (t=7 to t=9): position stays at 16 km → stopped
- E to F (t=10 to t=11): position stays at 8 km → stopped

> Answer: In all three intervals, the car is stopped (not moving).

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## ✔ Question 3: What is the car’s average velocity between “O” and “A”?

Average velocity = Δx / Δt = (24 km – 0 km) / (2 h – 0 h) = 12 km/h

> Answer: 12 km/h (away from detector)

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## ✔ Question 4: How long is the car stopped?

We add up the durations when position is constant (flat segments):

- A to B: 5 – 2 = 3 hours
- C to D: 9 – 7 = 2 hours
- E to F: 11 – 10 = 1 hour

Total stopped time = 3 + 2 + 1 = 6 hours

> Answer: 6 hours

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## ✔ Question 5: What is the car’s average velocity between “B” and “C”?

B: t=5, x=24 km
C: t=7, x=16 km

Δx = 16 – 24 = -8 km
Δt = 7 – 5 = 2 h

Average velocity = -8 km / 2 h = -4 km/h

(Negative means moving toward detector)

> Answer: -4 km/h (or 4 km/h toward the detector)

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## ✔ Question 6: What is the car’s average velocity between “D” and “E”?

D: t=9, x=16 km
E: t=10, x=8 km

Δx = 8 – 16 = -8 km
Δt = 10 – 9 = 1 h

Average velocity = -8 km / 1 h = -8 km/h

> Answer: -8 km/h (toward detector)

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## ✔ Question 7: How far did the car travel from “O” to “B”?

“Travel” usually means distance traveled, not displacement.

- O to A: moves from 0 → 24 km → distance = 24 km
- A to B: stationary → distance = 0 km

Total distance = 24 km

> Answer: 24 kilometers

*(Note: Displacement would also be 24 km, since it ended at 24 km from start.)*

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## ✔ Question 8: What is the car doing from “B” to “C” and “D” to “E”?

- B to C: position decreases from 24 km to 16 km → moving toward detector
- D to E: position decreases from 16 km to 8 km → moving toward detector

> Answer: In both intervals, the car is moving toward the detector.

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## ✔ Question 9: When is the car exceeding a 10 km/hr speed limit?

Speed = absolute value of velocity (since speed limit doesn’t care about direction).

Calculate velocity (slope) in each moving segment:

1. O to A: v = (24–0)/(2–0) = 12 km/h → exceeds 10 km/h
2. B to C: v = (16–24)/(7–5) = -8 km/h → speed = 8 km/h → under limit
3. D to E: v = (8–16)/(10–9) = -8 km/h → speed = 8 km/h → under limit
4. F to G: v = (24–8)/(15–11) = 16/4 = 4 km/h → under limit

Only O to A exceeds 10 km/h.

Time interval: from t=0 to t=2 hours

> Answer: The car exceeds the 10 km/hr speed limit between 0 and 2 hours.

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## 📌 Final Summary of Answers:

1. From O to A: moving away; from F to G: moving away.
2. Between A-B, C-D, E-F: car is stopped.
3. Average velocity O to A: 12 km/h
4. Total stopped time: 6 hours
5. Average velocity B to C: -4 km/h
6. Average velocity D to E: -8 km/h
7. Distance from O to B: 24 km
8. From B to C and D to E: moving toward detector.
9. Exceeding 10 km/h: between 0 and 2 hours

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✔ All questions solved with explanations! Let me know if you’d like graphs or visual aids too.