uniform circular motion (here the Latin d
was used instead of the Greek Δ
Using the figure we define the distance traveled by a particle during a brief time interval, , and the (vector) change in velocity:
1 , and
2 (rate times time equals distance).
3 (definition of acceleration).
4 (taking the absolute value of both sides).
5 (by similar triangles). Substituting (2) and (4) yields:
6 , which leads to , and therefore: