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.
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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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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