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It is because it moves at a uniform speed at the same period of time.

A particle under UCM covers a constant distance in completing circular trajectory in one revolution, which is equal to the perimeter of the circle.

s=2πr

Further the particle covers the perimeter with constant speed. It means that the particle travels the circular trajectory in a constant time given by its time period as :

T=2πr/v.

Hope i helped u:)