An object is moving along a horizontal line such that it's velocity is V(t) : = What is the object's displacement between t = 0 and t = 5? O 1.558 O 1.944 2.558 O 2.944 3 (3t+4)*
An object is moving along a horizontal line such that it's velocity is V(t) : = What is the object's displacement between t = 0 and t = 5? O 1.558 O 1.944 2.558 O 2.944 3 (3t+4)*
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Problem Description
An object is moving along a horizontal line with its velocity given by the equation \( V(t) = \frac{3}{(3t + 4)} \).
### Question
What is the object's displacement between \( t = 0 \) and \( t = 5 \)?
- \( 1.558 \)
- \( 1.944 \)
- \( 2.558 \)
- \( 2.944 \)
### Explanation
To find the object's displacement over the given time interval, you need to integrate the velocity function \( V(t) \) with respect to time \( t \) from \( t = 0 \) to \( t = 5 \).
The displacement \( s \) can be found as follows:
\[ s = \int_0^5 V(t) \, dt = \int_0^5 \frac{3}{3t + 4} \, dt \]
Use integration techniques to solve this definite integral. The correct answer will correspond to one of the provided options.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a92b920-e019-446e-b580-35fb69c82c25%2F56f9bc8d-ce5c-4693-80ca-1e7a3806945c%2Fg1pdpba_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Description
An object is moving along a horizontal line with its velocity given by the equation \( V(t) = \frac{3}{(3t + 4)} \).
### Question
What is the object's displacement between \( t = 0 \) and \( t = 5 \)?
- \( 1.558 \)
- \( 1.944 \)
- \( 2.558 \)
- \( 2.944 \)
### Explanation
To find the object's displacement over the given time interval, you need to integrate the velocity function \( V(t) \) with respect to time \( t \) from \( t = 0 \) to \( t = 5 \).
The displacement \( s \) can be found as follows:
\[ s = \int_0^5 V(t) \, dt = \int_0^5 \frac{3}{3t + 4} \, dt \]
Use integration techniques to solve this definite integral. The correct answer will correspond to one of the provided options.
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