Find the position vector for a particle with acceleration, initial velocity, and initial position given below. ā(t) = (3t, 6 sin(t), cos(5t)) v(0) = ( − 3, — 1,0) - 7(0) = (0, – 5,0) - r(t) =
Find the position vector for a particle with acceleration, initial velocity, and initial position given below. ā(t) = (3t, 6 sin(t), cos(5t)) v(0) = ( − 3, — 1,0) - 7(0) = (0, – 5,0) - r(t) =
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter5: Trigonometric Functions: Right Triangle Approach
Section5.1: Angle Measure
Problem 4E: Object A is travelling along a circle of radius 2, and Object B is travelling along a circle of...
Related questions
Question
![### Problem Statement:
Find the position vector for a particle with acceleration, initial velocity, and initial position given below.
### Given Data:
**Acceleration:**
\[
\vec{a}(t) = \langle 3t, 6 \sin(t), \cos(5t) \rangle
\]
**Initial Velocity:**
\[
\vec{v}(0) = \langle -3, -1, 0 \rangle
\]
**Initial Position:**
\[
\vec{r}(0) = \langle 0, -5, 0 \rangle
\]
### Required Solution:
**Position Vector:**
\[
\vec{r}(t) = \left\{\begin{array}{c}
\ \text{[enter x-component here]}\ , \\
\ \text{[enter y-component here]}\ , \\
\ \text{[enter z-component here]}\
\end{array}\right\}
\]
### Explanation:
You need to determine the position vector \(\vec{r}(t)\) by integrating the given acceleration vector \(\vec{a}(t)\) to find the velocity vector \(\vec{v}(t)\), and then integrating \(\vec{v}(t)\) to find the position vector \(\vec{r}(t)\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4962ae7-1cb2-4276-8f6a-b9f851b67289%2F0f94e9f9-b55f-4cfc-ae81-17b5ccf2df50%2Fswu57b_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
Find the position vector for a particle with acceleration, initial velocity, and initial position given below.
### Given Data:
**Acceleration:**
\[
\vec{a}(t) = \langle 3t, 6 \sin(t), \cos(5t) \rangle
\]
**Initial Velocity:**
\[
\vec{v}(0) = \langle -3, -1, 0 \rangle
\]
**Initial Position:**
\[
\vec{r}(0) = \langle 0, -5, 0 \rangle
\]
### Required Solution:
**Position Vector:**
\[
\vec{r}(t) = \left\{\begin{array}{c}
\ \text{[enter x-component here]}\ , \\
\ \text{[enter y-component here]}\ , \\
\ \text{[enter z-component here]}\
\end{array}\right\}
\]
### Explanation:
You need to determine the position vector \(\vec{r}(t)\) by integrating the given acceleration vector \(\vec{a}(t)\) to find the velocity vector \(\vec{v}(t)\), and then integrating \(\vec{v}(t)\) to find the position vector \(\vec{r}(t)\).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 6 steps with 6 images
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question
1/2-1/25cos(5t) is wring could you please check it again? thank you!
Solution
by Bartleby ExpertRecommended textbooks for you
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning