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\newcommand{\un}{\underline}
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\begin{center}
\textbf{Vector Functions and Curves}

\textit{\textbf{One variable functions}}
\end{center}

\textbf{Question}

Find the velocity, speed and acceleration of the particle with
position given by $\un{r}(t)$ at time
$t$. Also determine the particles path.

$$\underline{r}= a\cos t\underline{i}+ a\sin t\underline{j}+
ct\underline{k}$$

\textbf{Answer}

Position: $\underline{r}=a\cos t\underline{i}+ a\sin t\underline{j}
+ct\underline{k}$ 

Velocity: $\underline{v}=-a\sin t\underline{i} +a\cos t \underline{j}
+c\underline{k}$

Speed: $\it{v}=\sqrt{a^2+c^2}$

Acceleration: $\underline{a}=-a\cos t\underline{i} -a\sin t
\underline{j}$

Path: a circular helix.

\end{document}