Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![Use the given acceleration function and initial conditions to find the velocity vector \(\mathbf{v}(t)\), and position vector \(\mathbf{r}(t)\). Then find the position at time \(t = 2\).
\[
\mathbf{a}(t) = e^{t} \mathbf{i} - 4\mathbf{k}
\]
\[
\mathbf{v}(0) = 2\mathbf{i} + 3\mathbf{j} + \mathbf{k}, \quad \mathbf{r}(0) = \mathbf{0}
\]
\[
\mathbf{v}(t) = \underline{\hspace{5cm}}
\]
\[
\mathbf{r}(t) = \underline{\hspace{5cm}}
\]
\[
\mathbf{r}(2) = \underline{\hspace{5cm}}
\]](https://content.bartleby.com/qna-images/question/18936370-e2cc-46bd-a4d0-3c2ee0736afc/63fc9dc0-f8bd-46fb-a1a4-efca03f09ac1/4grxai_processed.png)
Transcribed Image Text:Use the given acceleration function and initial conditions to find the velocity vector \(\mathbf{v}(t)\), and position vector \(\mathbf{r}(t)\). Then find the position at time \(t = 2\).
\[
\mathbf{a}(t) = e^{t} \mathbf{i} - 4\mathbf{k}
\]
\[
\mathbf{v}(0) = 2\mathbf{i} + 3\mathbf{j} + \mathbf{k}, \quad \mathbf{r}(0) = \mathbf{0}
\]
\[
\mathbf{v}(t) = \underline{\hspace{5cm}}
\]
\[
\mathbf{r}(t) = \underline{\hspace{5cm}}
\]
\[
\mathbf{r}(2) = \underline{\hspace{5cm}}
\]
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