- 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 $v(t).$ $$ \begin{align*} \textbf{r}(t) = 3t\cos t\mathbf{i} + 3t\sin t\mathbf{j} + 4t\,\mathbf{k} \end{align*} $$
- $$ \begin{align*} \mathbf{v}(t) &= (3\,\text{cos}\,t - 3t\,\text{sin}\,t)\, \mathbf{i} + (3\,\text{sin}\,t + 3t\,\text{cos}\,t)\,\mathbf{j} + 4\,\textbf{k} \\ \mathbf{a}(t) &= (-6\,\text{sin}\,t - 3t\,\text{cos}\,t)\,\mathbf{i} + (6\,\text{cos}\,t - 3t\,\text{sin}\,t)\,\mathbf{j} \\ v(t) &= \sqrt{9t^2 + 25} \end{align*} $$