A body is in simple harmonic motion with time period half second (T=0.5s) and amplitude one cm (A=1cm). Find the average velocity in the interval in which it moves from equilibrium position to half of its amplitude.

Average velocity is simply the displacement of the particle divided by time taken.
Simple harmonic motion can be described by
x=Asinωt
where ω=2πT
if the particle starts at the mean position at t=0
time when particle reaches x=A/2 is when ωt=π/6 which is t=1/24 seconds
Total displacement is A/2
Hence average velocity = (A/2)/(1/24s) = 12cm/s