https://file.aiquickdraw.com/mathbot/file/1725982356985o33e03t6.jpg

Let's analyze the speed-time graph shown in the image and answer the questions from Exercise 21.8.

### a) What is the speed at:
1. **9:00?**  
   At 9:00, the speed is **0 km/h** (the graph starts from the origin).
   
2. **9:30?**  
   At 9:30, the speed is **3 km/h**.
   
3. **10:00?**  
   At 10:00, the speed is **6 km/h**.
   
4. **10:40?**  
   At 10:40, the speed is **0 km/h** (the graph drops to the time axis).

### b) Describe what is happening from 10:00 to 10:30.
From 10:00 to 10:30, the speed remains constant at **6 km/h**. This indicates that the object is moving at a steady speed without any acceleration or deceleration during this time period.

### c) What distance was traveled from:
1. **9:15 to 9:30?**  
   To find the distance, we use the formula:  
   \[
   \text{Distance} = \text{Speed} \times \text{Time}
   \]  
   From 9:15 to 9:30, the speed changes linearly from 0 to 3 km/h, forming a triangle. The time is 15 minutes (0.25 hours).  
   Distance = \(\frac{1}{2} \times 3 \times 0.25 = 0.375 \text{ km}\).

2. **10:20 to 10:30?**  
   During this time, the speed is constant at 6 km/h for 10 minutes (0.1667 hours).  
   Distance = \(6 \times 0.1667 = 1 \text{ km}\).

3. **9:00 to 11:30?**  
   This involves multiple segments:  
   - From 9:00 to 9:30: Speed increases from 0 to 3 km/h.
   - From 9:30 to 10:00: Speed increases from 3 to 6 km/h.
   - From 10:00 to 10:30: Speed is constant at 6 km/h.
   - From 10:30 to 11:00: Speed decreases to 2 km/h.
   - From 11:00 to 11:30: Speed increases to 6 km/h.

   Total distance calculation:
   - From 9:00 to 9:30: Distance = \(0.375 \text{ km}\).
   - From 9:30 to 10:00: Distance = \(\frac{1}{2} \times (3 + 6) \times 0.5 = 2.25 \text{ km}\).
   - From 10:00 to 10:30: Distance = \(6 \times 0.5 = 3 \text{ km}\).
   - From 10:30 to 11:00: Distance = \(\frac{1}{2} \times (6 + 2) \times 0.5 = 2 \text{ km}\).
   - From 11:00 to 11:30: Distance = \(\frac{1}{2} \times (2 + 6) \times 0.5 = 2 \text{ km}\).

   Total Distance = \(0.375 + 2.25 + 3 + 2 + 2 = 9.625 \text{ km}\).

Would you like more details or have any questions?

### Related Questions:
1. How can we calculate the total time taken for each segment of the journey?
2. What is the average speed over the entire period from 9:00 to 11:30?
3. How would the graph change if the object decelerated uniformly after 11:00?
4. What does the area under the speed-time graph represent?
5. How would you describe the motion from 10:30 to 11:00?

**Tip:** Remember that the area under a speed-time graph represents the distance traveled.

Study this speed-time graph and answer the questions from Exercise 21.8.

Learn how to analyze a speed-time graph to determine speed at specific times and calculate distances traveled. Exercise 21.8 covers concepts like constant speed, deceleration, and calculating areas under the graph to find total distance.

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