A1.0 kg mass is attached to the end of a 1.00 m long string and swung in a horizontal circle. if the mass completes one cycle in 0.42 s, the speed of the mass is

Since the mass is moving in a horizontal circle, we do not look at gravity, tension in string or weight of the mass.

Time period for one cycle around circle = T = 0.42 seconds

Tangential Velocity or speed of the mass =
         tangential distance traveled in 1 cycle or revolution / time period
        = circumference of circle / time period
       = 2 π radius / T  = 2 π 1 meter / 0.42 sec 
       =  14.96 m/s