\[ v_{\text{avg}} = \frac{\Delta\text{position}}{\Delta t} \]
\begin{align*}
\text{speed} &= |{\text{velocity}}| \\
- &= \sqrt{v_x(t)^2 + v_y(t)^2 + v_z(t)^2} \tag{for vector \(v\)}
+ &= \sqrt{v_x^2 + v_y^2 + v_z^2}
\end{align*}
- \textbf{Distance travelled between\(t=a \rightarrow t=b\):}
+ \textbf{Distance travelled between \(t=a \rightarrow t=b\):}
\[= \int^b_a \sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2} \cdot dt \]
\subsection*{Vector functions}