Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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### Vehicle Position Analysis

Two vehicles start out traveling side by side along a straight road. Their position functions, shown in the following graph, are given by \( s = f(t) \) and \( s = g(t) \), where \( s \) is measured in meters and \( t \) is measured in seconds.

![Graph](image-url) 
*Graph Description:*
- The graph features two curves titled \( s = f(t) \) (blue curve) and \( s = g(t) \) (green curve).
- The horizontal axis represents time \( t \) measured in seconds, ranging from 0 to 5 seconds.
- The vertical axis represents position \( s \) measured in meters, ranging from -1 to 10 meters.
- Both curves start at the origin (0,0) and depict different rates of position change over time.

#### Questions:

1. **Which vehicle has traveled farther at \( t = 2 \) seconds?**
    - ☐ Vehicle \( f \)
    - ☐ Vehicle \( g \)

2. **What is the approximate velocity of the \( f \) vehicle at \( t = 3 \) seconds?**
    - ☐ ______ meters per second

3. **What is the approximate velocity of the \( g \) vehicle at \( t = 3 \) seconds?**
    - ☐ ______ meters per second

4. **Which vehicle is traveling faster at \( t = 4 \) seconds?**
    - ☐ Vehicle \( f \)
    - ☐ Vehicle \( g \)

### Explanation of Graph:
- At \( t = 2 \) seconds, compare the values of \( s \) on the blue and green curves.
- Approximate the slopes of both the \( f(t) \) and \( g(t) \) curves at \( t = 3 \) seconds to determine their velocities.
- At \( t = 4 \) seconds, visually observe the slope steepness of both curves to decide which vehicle is traveling faster.
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Transcribed Image Text:### Vehicle Position Analysis Two vehicles start out traveling side by side along a straight road. Their position functions, shown in the following graph, are given by \( s = f(t) \) and \( s = g(t) \), where \( s \) is measured in meters and \( t \) is measured in seconds. ![Graph](image-url) *Graph Description:* - The graph features two curves titled \( s = f(t) \) (blue curve) and \( s = g(t) \) (green curve). - The horizontal axis represents time \( t \) measured in seconds, ranging from 0 to 5 seconds. - The vertical axis represents position \( s \) measured in meters, ranging from -1 to 10 meters. - Both curves start at the origin (0,0) and depict different rates of position change over time. #### Questions: 1. **Which vehicle has traveled farther at \( t = 2 \) seconds?** - ☐ Vehicle \( f \) - ☐ Vehicle \( g \) 2. **What is the approximate velocity of the \( f \) vehicle at \( t = 3 \) seconds?** - ☐ ______ meters per second 3. **What is the approximate velocity of the \( g \) vehicle at \( t = 3 \) seconds?** - ☐ ______ meters per second 4. **Which vehicle is traveling faster at \( t = 4 \) seconds?** - ☐ Vehicle \( f \) - ☐ Vehicle \( g \) ### Explanation of Graph: - At \( t = 2 \) seconds, compare the values of \( s \) on the blue and green curves. - Approximate the slopes of both the \( f(t) \) and \( g(t) \) curves at \( t = 3 \) seconds to determine their velocities. - At \( t = 4 \) seconds, visually observe the slope steepness of both curves to decide which vehicle is traveling faster.
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