https://file.aiquickdraw.com/mathbot/file/1726264657566u358vbkp.jpg

To solve the problem of finding the average acceleration for the bus over the 3.5-hour period, we first need to understand the graph, which shows the position of the bus over time. The position is given in kilometers (km), and the time is in hours (h).

### Steps:

1. **Identify the relevant values from the graph**:
   - At \( t = 0 \), the position is \( x = 0 \) km.
   - At \( t = 3.5 \) hours, the position is \( x = 20 \) km.

2. **Calculate the velocity at different sections of the graph**:
   - **Average velocity** is calculated as the change in position divided by the change in time:
     \[
     v = \frac{\Delta x}{\Delta t}
     \]
     For the entire trip, the total change in position is \( \Delta x = 20 \, \text{km} - 0 \, \text{km} = 20 \, \text{km} \), and the total time is \( \Delta t = 3.5 \, \text{h} \).

3. **Calculate the average acceleration**:
   Since the question asks for **average acceleration**, we must calculate the change in velocity over time. 
   - However, this is a position-time graph, so to find acceleration, we would look at how the velocity changes. In the sections between \( A \), \( B \), and \( C \), the graph indicates changes in velocity due to the slope of the lines, but to simplify for average acceleration over the entire time:
     \[
     a_{\text{avg}} = \frac{\Delta v}{\Delta t}
     \]
     Since we need more details about the velocity at \( B \) and \( C \), we focus on the average acceleration over the total time period.

Let me know if you'd like further clarification or a breakdown of velocities at individual segments (A, B, C) from the graph.

Would you like a detailed calculation or explanation of each section's velocity? Here are 5 related questions:

1. How do you calculate average velocity from a position-time graph?
2. What does the slope of a position-time graph represent?
3. Can you determine instantaneous acceleration from this graph?
4. How would a velocity-time graph look for the same trip?
5. What units are commonly used for acceleration, and how are they derived?

**Tip:** The slope of a position-time graph gives the velocity at any point.

A bus makes a trip according to the position-time graph shown in the illustration. What is the average acceleration (in km/h²) of the bus for the entire 3.5-h period shown in the graph?

Explore how to calculate the average acceleration of a bus over a 3.5-hour trip using a position-time graph. This guide covers the calculation of average velocity and then the determination of acceleration, providing a clear method using calculus principles suitable for college students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation