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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.

$$\underline{r}= ae^t\underline{i}+ be^t\underline{j}+
ce^t\underline{k}$$

\textbf{Answer}

Position: $\underline{r}=ae^t\underline{i}+ be^t \underline{j}+ce^t
\underline{k}$ 

Velocity: $\underline{v}=\underline{r}$

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

Acceleration: $\underline{a}=\underline{v}=\underline{r}$

Path: the half-line $\frac{x}{a}=\frac{y}{b}=\frac{z}{c} >0$.


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