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

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Escape velocity is defined as the speed needed for an object to break free from a gravitational field, resulting in zero total energy at an infinite distance. At this point, both kinetic energy (KE) and potential energy (PE) are considered zero. The discussion highlights a common misunderstanding regarding kinetic energy, asserting that once an object reaches escape velocity, it retains that speed unless acted upon by another force. However, as the object moves away from the gravitational source, its kinetic energy decreases while potential energy approaches zero, ultimately leading to a total energy of zero at infinity. This illustrates the concept of limits in gravitational dynamics.
yasar1967
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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?
 
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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.
 

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