The velocity of a particle varies directly as the product of its position and time squared. The particle has known positions s(0) = 3 and s(2) = 5. Answer the following. 11) Write a differential equation that models this situation. Let s represent the position of the particle and t represent the time. I 12) Solve for the general solution. Write your answer as a function s(t). 13) Use the initial condition to find the constant of integration, then write the particular solution as a function s(t). 14) Use the second condition to find the constant of proportion. Round your answer to five decimal places. 15) Find the position of the particle at t = 3. Round your answer to three decimal places.
The velocity of a particle varies directly as the product of its position and time squared. The particle has known positions s(0) = 3 and s(2) = 5. Answer the following. 11) Write a differential equation that models this situation. Let s represent the position of the particle and t represent the time. I 12) Solve for the general solution. Write your answer as a function s(t). 13) Use the initial condition to find the constant of integration, then write the particular solution as a function s(t). 14) Use the second condition to find the constant of proportion. Round your answer to five decimal places. 15) Find the position of the particle at t = 3. Round your answer to three decimal places.
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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Question
![The velocity of a particle varies directly as the product of its position and time squared. The particle has
known positions s(0) = 3 and s(2) = 5. Answer the following.
H
11) Write a differential equation that models this situation. Let s represent the position of the particle and t
represent the time.
I
12) Solve for the general solution. Write your answer as a function s(t).
13) Use the initial condition to find the constant of integration, then write the particular solution as a
function s(t).
14) Use the second condition to find the constant of proportion. Round your answer to five decimal
places.
15) Find the position of the particle at t = 3. Round your answer to three decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd27ccdcd-ca2c-4ebc-862f-b9a4af9c7f08%2Fe84c27ec-1f4d-49f4-af4f-9dbb68dfda95%2F9999plm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The velocity of a particle varies directly as the product of its position and time squared. The particle has
known positions s(0) = 3 and s(2) = 5. Answer the following.
H
11) Write a differential equation that models this situation. Let s represent the position of the particle and t
represent the time.
I
12) Solve for the general solution. Write your answer as a function s(t).
13) Use the initial condition to find the constant of integration, then write the particular solution as a
function s(t).
14) Use the second condition to find the constant of proportion. Round your answer to five decimal
places.
15) Find the position of the particle at t = 3. Round your answer to three decimal places.
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