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\begin{center}
\textbf{Vector Functions and Curves}

\textit{\textbf{One variable functions}}
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\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.

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

\textbf{Answer}

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

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

Speed: $\it{v}=\sqrt{4t^2+1}$

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

Path: the parabola $y=z^2$ in the plane $x=0$.

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