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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.

$$\underline{r}= 3\cos t\underline{i}+ 4\sin t\underline{j}+
t\underline{k}$$

\textbf{Answer}

Position: $\underline{r}=3\cos t \underline{i} +4\sin t\underline{j}
+t\underline{k}$

Velocity: $\underline{v}=-3\sin t \underline{i} +4\cos t \underline{j}
+\underline{k}$

Speed: $\it{v}=\sqrt{9\sin^2t+16\cos^2t+1}=\sqrt{10+7\cos^2t}$

Acceleration: $\underline{a}=-3\cos t \underline{i} -4\sin
t\underline{j}= t\underline{k}-\underline{r}$

Path: a helix wound around the elliptical cylinder $(x^2/9)+(y^2/16)=1$.


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