Consider the following problem from Science: A mitochondria with velocity vector r' (t) starts out at (-4, 0, 5) at t = 0 and mitochondrias around for 5 seconds. Where is the mitochondria located at time t = 5 if Ir' (t)| dt = 0? A) (-4, 0, 5) B) (-4, 0,5) C) (3, 0, 7) 6. D) Not enough information
Consider the following problem from Science: A mitochondria with velocity vector r' (t) starts out at (-4, 0, 5) at t = 0 and mitochondrias around for 5 seconds. Where is the mitochondria located at time t = 5 if Ir' (t)| dt = 0? A) (-4, 0, 5) B) (-4, 0,5) C) (3, 0, 7) 6. D) Not enough information
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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Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.
Question
Transcribed Image Text:### Science Problem: Mitochondria Location Over Time
Consider the following problem from Science: A mitochondria with velocity vector \(\mathbf{r}'(t)\) starts out at \((-4, 0, 5)\) at \(t = 0\) and mitochondrias around for 5 seconds. Where is the mitochondria located at time \(t = 5\) if \(\int_0^5 |\mathbf{r}'(t)| \, dt = 0\)?
**Options:**
A) \((-4, 0, 5)\)
B) \(\langle -4, 0, 5 \rangle\)
C) \((3, 0, 7)\)
D) Not enough information
**Answer Choices for Selection:**
- ⃝ D
- ⃝ B
- ⃝ A
- ⃝ C
### Clarification of the Problem:
The problem involves determining the position of a mitochondria given its initial velocity and starting coordinates. The velocity vector's integral being zero over the given timeframe suggests that there has been no change in position.
### Additional Notes:
- The notation \((-4, 0, 5)\) and \(\langle -4, 0, 5 \rangle\) typically represent the same point in space but are written using different notational conventions. This problem can serve as an example to reinforce understanding of vector notation in different contexts.
- Since the integral of the magnitude of the velocity vector over the given time frame is zero, it indicates that the mitochondria did not move from its initial position.
### Interpretation of Graphs/Diagrams:
The problem does not include graphs or diagrams. The primary explanation revolves around understanding notations and integrals in relation to motion.
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