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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.

$$\underline{r}=t^2\underline{i}-t^2\underline{j}+\underline{k}$$

\textbf{Answer}

Position: $\underline{r}=t^2\underline{i}- t^2\underline{j}+
\underline{k}$

Velocity: $\underline{v}=2t\underline{i}- 2t\underline{j}$

Speed: $\it{v}=2\sqrt{2}t$

Acceleration: $\underline{a}=2\underline{i} -2\underline{j}$

Path: the half-line $x=-y\ge 0$, $z=1$.



\end{document}