how are you differentiating it? as it contains two variables.
Let us take y=Asin(kx-wt)
at t=0, the shape of the curve is y=Asinkx at x=0, the disp is zero
Now v of any particle = ∂y/∂t = -Awcos(kx-wt)
At t=0, v = -Awcoskx
vel of the particle at x=0 is -Aw i.e. it is moving downward
by Asin(kx-wt) this one is moving upwards
u need to get the time intervals and the position of the particle you are talking about.
AT any instant of time there will be some particles moving upward, some particles moving downward and some at rest..
btw hows the prep for NSEP going on?? completed everything??