Using the figure we define the distance traveled by a particle during a brief time interval,
, and the (vector) change in velocity:
uniform circular motion (here the Latin d was used instead of the Greek Δ
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:
7