The given diagram explains the situation...
Since the body moves with no force....So <mod>F = mg
So <mod> v x A = mg
=> vA sin <theta> = mg
=> v = mg / [A sin <theta>]
Now v is minimum if R.H.S. is minimum and
R.H.S. is minimum if<theta> is 900 such that sin <theta> = 1...which makes the denominator maximum and so the R.H.S. minimum
So vminimum = mg/A