https://file.aiquickdraw.com/mathbot/file/17262654983922j70aceq.jpg

Let's analyze the problem based on the image provided. The graph is a position-time graph, and we are asked to find the average velocity (in km/h) during the three segments A, B, and C of the bus's journey.

### Steps to solve:
The average velocity \( v_{\text{avg}} \) for each segment is calculated as:

\[
v_{\text{avg}} = \frac{\Delta x}{\Delta t}
\]

Where:
- \( \Delta x \) is the change in position (displacement),
- \( \Delta t \) is the change in time.

Now, let's break down each segment:

#### Segment A (0 to 1 hour):
- Initial position: \( x_i = 40 \, \text{km} \)
- Final position: \( x_f = 0 \, \text{km} \)
- Time interval: \( t = 1.0 \, \text{hour} \)

\[
v_{\text{avg}}(A) = \frac{x_f - x_i}{t} = \frac{0 - 40}{1.0} = -40 \, \text{km/h}
\]
However, the user entered \(-16.67 \, \text{km/h}\), which seems incorrect, as the correct velocity should be \(-40 \, \text{km/h}\).

#### Segment B (1 to 2 hours):
- Initial position: \( x_i = 0 \, \text{km} \)
- Final position: \( x_f = -20 \, \text{km} \)
- Time interval: \( t = 1.0 \, \text{hour} \)

\[
v_{\text{avg}}(B) = \frac{x_f - x_i}{t} = \frac{-20 - 0}{1.0} = -20 \, \text{km/h}
\]
The user entered \(10 \, \text{km/h}\), which is also incorrect; the correct value should be \(-20 \, \text{km/h}\).

#### Segment C (2 to 3 hours):
- Initial position: \( x_i = -20 \, \text{km} \)
- Final position: \( x_f = 40 \, \text{km} \)
- Time interval: \( t = 1.0 \, \text{hour} \)

\[
v_{\text{avg}}(C) = \frac{x_f - x_i}{t} = \frac{40 - (-20)}{1.0} = \frac{60}{1} = 60 \, \text{km/h}
\]
The user entered \(40 \, \text{km/h}\), but the correct velocity should be \(60 \, \text{km/h}\).

### Summary of Correct Answers:
- (a) \( v_{\text{avg}}(A) = -40 \, \text{km/h} \)
- (b) \( v_{\text{avg}}(B) = -20 \, \text{km/h} \)
- (c) \( v_{\text{avg}}(C) = 60 \, \text{km/h} \)

Would you like further details on any step, or have any questions?

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Here are 5 related questions you could explore:
1. How do you determine displacement from a position-time graph?
2. What is the difference between average velocity and average speed?
3. How do you calculate velocity if the graph is non-linear?
4. How can you interpret positive vs negative velocities on a graph?
5. How is instantaneous velocity different from average velocity?

**Tip**: Always keep in mind that velocity is a vector quantity, meaning it has both magnitude and direction.

A bus makes a trip according to the position-time graph shown. What is the average velocity (magnitude and direction) of the bus during segment A, segment B, and segment C? Express your answers in km/h.

Learn how to calculate the average velocity of a bus from a position-time graph in segments A, B, and C. This problem covers key kinematic concepts, including calculating velocity using displacement and time. Suitable for high school students in Grades 10-12.

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