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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.

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


\textbf{Answer}

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

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

Speed: $\it{v}=\sqrt{1+8t^2}$

Acceleration: $\underline{a}=2\underline{j}+ 2\underline{k}$

Path: the parabola $y=z=x^2$.


\end{document}