We define the change in a vector as ΔA = 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 = Δv/Δt. That is, the vector a over the interval Δt points in the direction of Δv. And Δv is just the vector which, when added to the initial velocity v, gives the new velocity v'. That is, v' = v + Δv. It is absolutely vital to understand this perfectly and completely!!!!