Question

To introduce you to the concept of escape velocity for a rocket. the escape velocity is defined to be the minimum speed with which an object of mass m must move to escape from the gravitational attraction of a much larger body, such as a planet of total mass m. the escape velocity is a function of the distance of the object from the center of the planet r, but unless otherwise specified this distance is taken to be the radius of the planet because it addresses the question "how fast does my rocket have to go to escape from the surface of the planet?"

Answer 1

All of that may very well be true. But I'm still left to wonder whether you have a question to ask.

Answer 2

A projectile fired upward from the Earth's surface will usually slow down, come momentarily to rest, and return to Earth. For a certain initial speed, however it will move upward forever, with its speed gradually decreasing to zero just as its distance from Earth approaches infinity. The initial speed for this case is called escape velocity. You can find the escape velocity v for the Earth or any other planet from which a projectile might be launched using conservation of energy. The projectile of mass m leaves the surface of the body of mass M and radius R with a kinetic energy Ki = mv²/2 and potential energy Ui = -GMm/R. When the projectile reaches infinity, it has zero potential energy and zero kinetic energy since we are seeking the minimum speed for escape. Thus Uf = 0 and Kf = 0. And from conservation of energy,
Ki + Ui = Kf + Uf
mv²/2 -GMm/R = 0
∴ v = √(2GM/R) 

This is the expression for escape velocity.