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 $.

a(t) = acceleration at time tv(t) = velocity at time ts(t) = position at time t Given: a(t) =…

Answered: Given the acceleration, initial…

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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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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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 $.

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