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Find Position, Velocity and Acceleration Vectors Find the velocity vector for the position vector r(t) = (sin(12t), 5t7, e−5t). x component = y component z component Submit Question

Find Position, Velocity and Acceleration Vectors Find the velocity vector for the position vector r(t) = (sin(12t), 5t7, e−5t). x component = y component z component Submit Question

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Find Position, Velocity, and Acceleration Vectors **Problem Statement:** Find the velocity vector for the position vector \(\vec{r}(t) = \langle \sin(12t), 5t^7, e^{-5t} \rangle\). **Components to Determine:** - **x component:** - **y component:** - **z component:** Buttons: - **Submit Question** **Instructions:** To determine the velocity vector, differentiate each component of the position vector \(\vec{r}(t)\) with respect to time \(t\). **Hints for Students:** - The x component is the derivative of \(\sin(12t)\). - The y component is the derivative of \(5t^7\). - The z component is the derivative of \(e^{-5t}\). Fill in the blanks with the correct derivatives to find the velocity vector, and submit your answer by clicking the "Submit Question" button.
Transcribed Image Text:### Find Position, Velocity, and Acceleration Vectors **Problem Statement:** Find the velocity vector for the position vector \(\vec{r}(t) = \langle \sin(12t), 5t^7, e^{-5t} \rangle\). **Components to Determine:** - **x component:** - **y component:** - **z component:** Buttons: - **Submit Question** **Instructions:** To determine the velocity vector, differentiate each component of the position vector \(\vec{r}(t)\) with respect to time \(t\). **Hints for Students:** - The x component is the derivative of \(\sin(12t)\). - The y component is the derivative of \(5t^7\). - The z component is the derivative of \(e^{-5t}\). Fill in the blanks with the correct derivatives to find the velocity vector, and submit your answer by clicking the "Submit Question" button.
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