Why is final kinetic energy zero?
From a comment by the original poster, "this is regarding escape velocity".
The answer is simple: That's how escape velocity is defined.
Gravitational potential energy is always non-positive and is only zero at an infinite distance. Kinetic energy is always non-negative and is only zero when the relative velocity is zero. This means that the total energy, gravitational potential energy plus kinetic energy, of a pair of objects orbiting one another can be negative, positive, or zero. This total energy is a constant in Newtonian mechanics.
If the total energy is negative the objects remain forever bound to one another. They don't escape. They instead follow elliptical or circular orbits about one another.
If the total energy is positive the objects do escape from one another and eventually (in an infinite amount of time) become separated by an infinite distance. The objects follow hyperbolic arcs as they separate. Gravitational potential energy drops to zero at an infinite distance, but since total energy is conserved, the kinetic energy must be positive even at this infinite separation.
Finally, if the total energy of the system is exactly zero, the objects do escape from one another following parabolic arcs. Eventually (in an infinite amount of time at an infinite distance), the gravitational potential becomes zero, just as it does when the total energy is positive. Since the total energy is constantly zero, the kinetic energy must also become zero at an infinite distance in this case.
This special case of zero total energy is how escape velocity is defined. It's a very useful but unachievable concept. Useless concepts in science tend to be discarded. Escape velocity is unachievable in the sense that the probability of obtaining exactly zero total energy is exactly zero. However, the concept is very useful and is easy to calculate. Equal or exceed this easily calculable velocity and you escape. Don't exceed it and you don't escape.