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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.

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

\textbf{Answer}

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

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

Speed: $\it{v}=|a\omega |$

Acceleration: $\underline{a}=-a\omega^2\cos\omega t\underline{i}-
a\omega^2 \sin\omega t \underline{k}$

Path: the circle $x^2+z^2=a^2$, $y=b$.

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