### Science Problem: Mitochondria Location Over TimeConsider 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.

Answered: Image /qna-images/answer/bbe05530-fc6b-46bf-a194-75ce10dc6c5d.jpg

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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Concept explainers

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.

Question

### 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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