- Calculus, Volume 1: One Variable Calculus, with an Introduction to Linear Algebra
- Tom M. Apostol
- Second Edition
- 1967
- 978-1-119-49673-1
14.7 Exercises
- In each of Exercises 1 through 6, $\textbf{r}(t)$ denotes the position vector at time $t$ for a particle moving on a space curve. Determine the velocity $\textbf{v}(t)$ and acceleration $\textbf{a}(t)$ in terms of $\mathbf{i}, \mathbf{j}, \mathbf{k};$ also, compute the speed $v(t).$ $$ \begin{align*} \\ \textbf{r}(t) = \cos t\,\mathbf{i} + \sin t\,\mathbf{j} + e^t\,\mathbf{k} \end{align*} $$
- $$ \begin{align*} \textbf{v}(t) &= -\text{sin}\,t\,\textbf{i} + \text{cos}\,t\,\textbf{j} + e^t\,\textbf{k} \\ \\ \textbf{a}(t) &= -\text{cos}\,t\,\textbf{i} - \text{sin}\,t\,\textbf{j} + e^t\,\textbf{k} \\ \\ v(t) &= \left(1 + e^{2t}\right)^{1/2} \end{align*} $$