Explaining Escape Velocity: Zero KE and PE at r=infinite

[yasar1967]

Escape Velocity:
"An object given the escape speed will have zero kinetic energy at r=infinite, and the potential energy is defined to be zero at that point, so the total energy is 0"

I understand having zero potential energy at infinite distance but I do not correlate with having zero kinetic energy. Once you have given that escape velocity to the object it must have always that speed even even at the infinity unless another force is applied. So how could it be that it's kinetic energy will be zero?

 

[dst]

The kinetic energy decreases to zero as the potential decreases to zero (because it is accelerating, against gravity). Gravity causes it to decrease (i.e. the escape velocity is the minimum needed to escape the field). Just a case of a limit.