We define the change in a vector
as Δ**A** = **A**_{final} - **A**_{initial},
so that if we examine a changing velocity we can visually estimate the direction
of the acceleration **a** instantly, using the concept that **a** =
Δ**v**/Δt. That is, the vector **a** over the interval
Δt points in the direction of Δ**v**. And Δ**v**
is just the vector which, when added to the initial velocity **v**, gives
the new velocity **v'**. That is, **v'** = **v** + Δ**v**.
It is * absolutely vital to understand this perfectly and completely!!!!*