https://latex.codecogs.com/eqneditor/editor.php

\\
d_b := \text{cumulated branch length}
\\
\Delta t:= \text{branch duration}
\\
k:=\text{number of spots of branch}
\\
\vec{s_{i}} = i^{th}\text{spot of branch}
\\
tp_{s_i} = \text{time point of } i^{th}\text{spot}\text{ of branch}
\\
\Delta t=tp_{s_k} - tp_{s_1}
\\
d_b=\sum_{i=1}^{k-1} \left | \vec{s_{i+1}} - \vec{s_{i}} \right|
\\
\overline{v_b} := \text{average movement of branch}
\\
\overline{v_b} = \frac{d_b} {\Delta t}
