Given the acceleration, initial velocity, and initial position of a body moving along a coordinate line at time t, find the body's position at time t. a = 32 cos 5t, v(0) = -9, s(0) = -5 %3D
Given the acceleration, initial velocity, and initial position of a body moving along a coordinate line at time t, find the body's position at time t. a = 32 cos 5t, v(0) = -9, s(0) = -5 %3D
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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how do i solve. i am so confused. maybe what is the formula i am supposed to use. this is my last hw of the summer
![### Problem Solving Exercise: Finding the Position of a Body in Motion
**Problem Statement:**
Solve the problem.
Given the acceleration, initial velocity, and initial position of a body moving along a coordinate line at time \( t \), find the body's position at time \( t \).
- Acceleration (\(a\)): \( 32 \cos 5t \)
- Initial Velocity (\(v(0)\)): \( 9 \)
- Initial Position (\(s(0)\)): \( -5 \)
**Graphical Representation:**
There are no graphs or diagrams provided in the problem statement.
**Explanation:**
To solve this problem, you need to integrate the acceleration function to find the velocity function and then integrate the velocity function to find the position function.
1. **First Integration (from acceleration to velocity):**
\[ \int a \, dt \to v(t) \]
2. **Second Integration (from velocity to position):**
\[ \int v(t) \, dt \to s(t) \]
Using the initial conditions, you will be able to determine the constants of integration for both integrations. This will provide you with the body's position at any time \( t \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F670cec44-172f-4f6c-8b5b-add8e60675be%2F7dc2c2bf-4373-41c2-a976-ac0734847047%2Fnrbdlvo.png&w=3840&q=75)
Transcribed Image Text:### Problem Solving Exercise: Finding the Position of a Body in Motion
**Problem Statement:**
Solve the problem.
Given the acceleration, initial velocity, and initial position of a body moving along a coordinate line at time \( t \), find the body's position at time \( t \).
- Acceleration (\(a\)): \( 32 \cos 5t \)
- Initial Velocity (\(v(0)\)): \( 9 \)
- Initial Position (\(s(0)\)): \( -5 \)
**Graphical Representation:**
There are no graphs or diagrams provided in the problem statement.
**Explanation:**
To solve this problem, you need to integrate the acceleration function to find the velocity function and then integrate the velocity function to find the position function.
1. **First Integration (from acceleration to velocity):**
\[ \int a \, dt \to v(t) \]
2. **Second Integration (from velocity to position):**
\[ \int v(t) \, dt \to s(t) \]
Using the initial conditions, you will be able to determine the constants of integration for both integrations. This will provide you with the body's position at any time \( t \).
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