I am trying to work out an equation without a description. I need to figure out what is this equation exactly and how to interpret its results. Here it is:
Variables:
$ u_1, u_2, u_3,... u_n [m] $
$ s_1, s_2, s_3,... s_n [m] $
$ v_1, v_2, v_3,... v_n [\frac{m}{s}] $
$ V, U [\frac{m}{s}] $
Calculations:
$ u_1 = s_1 \cdot \frac{(V - v_2) \cdot (V - v_3) \cdot ... \cdot (V - v_n)} {(v_1 - v_2) \cdot (v_1 - v_3) \cdot ... \cdot (v_1 - v_n)} $
$ u_2 = s_2 \cdot \frac{(V - v_1) \cdot (V - v_3) \cdot ... \cdot (V - v_n)} {(v_2 - v_1) \cdot (v_2 - v_3) \cdot ... \cdot (v_2 - v_n)} $
$ u_3 = s_3 \cdot \frac{(V - v_1) \cdot (V - v_2) \cdot ... \cdot (V - v_n)} {(v_3 - v_1) \cdot (v_3 - v_2) \cdot ... \cdot (v_3 - v_n)} $
$ \vdots $
$ u_n = s_n \cdot \frac{(V - v_1) \cdot (V - v_2) \cdot ... \cdot (V - v_n)} {(v_n - v_1) \cdot (v_n - v_2) \cdot ... } $
$ U = u_1 + u_2 + u_3 + ... + u_n $
In this example the $ s $ and $ u $ elements are lengths and $ v $ are velocities. $ v $ and $ s $ are velocity->distance pairs representing breaking distance of an object for a certain speed of that object. $ V $ is the current velocity of the object. What are $ u $ and $ U $?
I would appreciate all help regarding understanding this.