An object undergoing uniform circular motion is moving with a constant speed. Nonetheless, it is accelerating due to its change in direction. The direction of the acceleration is inwards.
and it depends upon case by case . 
but in most of the cases IF ACCELERATION IS CONSTANT THEN ITS A UNIFORM MOTION . 
hope it clears your doubt 
ALL THE BEST ..
 
						

							
Points to be remembered:
For the uniform motion the accleration should be zero.
and the velocity should be constant.
.
For constant accln. the motion can be vary.
It could be uniform or non – uniform depending upon the parametres. given. 
 
						

							
Constant acceleration is the special case of acceleration. When a moving body changes its velocity by the equal amount per second, the body is said to be moving with the constant acceleration.
Time(s)
	
		
			
Time(s)
			
Velocity (m)
		
		
			
1
			
2
		
		
			
2
			
4
		
		
			
3
			
6
		
		
			
4
			
8
		
		
			
5
			
			
10
			
		
	
in this box the velocity is constantly varying with same amount per second so the acceleration in this case is constant