is kinetic energy a function of average velocity or final?

Kinetic energy depends on the velocity at the exact moment in time (aka "instantaneous velocity") when the kinetic energy is being calculated so it is not necessarily based on average or final velocity.

The instantaneous velocity will eventually become the average and then the final velocity, but most of the time it will not be those.

good answer wilvin - to start with - then you blew it!.

The KE of a body moving in a straight line is given by E = 1/2 m v^2 where E and V are instantaneous values.

(it can also have ke due to rotation - even if it has no linear motion.)

Consider a pendulum. it continually trades potential energy for kinetic energy and vice versa.

NO. Momentum is a vector so that's 0 if the bodies are traveling in opposite guidelines mutually as kinetic capability is a scalar and is not 0 in such cases. think of of an exploding gadget. the completed momentum is 0 until now and after detonation however the ok.E is definetly not 0 as products of it are flying everywhere.

it really depends on the problem, it could potentially be both

Could be both.