Question

from where a arrow gets kinetic energy to go from bow

Answer 1

when we stretch the string by our muscular force, potential energy stored in it and when we shot an arrow all the potential energy convert into kinetic energy which transfer into the arrow.

Answer 2

When the string of bow is pulled, some work in done here which is stored in the form of elastic potential energy in the stretched string. This string when released changes the potential energy into kinetic energy which makes the arrow to move. 

Thus an arrow acquires its kinetic energy from the stretched string of a bow (elastic potential energy)