For a wave described by, `y = A sin(omega t -kx)`, consider the following points (i) x =0,(ii) `x =pi/(4k)`
For aparticle at each ofthese.points at t = 0, describe whether the particle is moving or not and in what direction and describe whether the particle is speeding up, slowing down or instantaneously not accelerating.

Explanation

`y =A sin(omegat -kx),` Particle velocity
`v_p (X,t) =(delta y)/(delta t) = omegaA cos (ometat -kx)`
and particle acceleration
`a_p (x,t) = (delta^2y)/(deltat^2) =- omega^2 A sin(omegat -kx)`
i) `t =0 ,x=0 : v_p =+omegaA and a_p =0` i.e., particle is moving upwards but its acceleration is zero.
ii) At `t =0, x = pi/(4k), V_p =(A omega)/(sqrt2)`, upward and
`a_p =(omega^2A)/sqrt2` upward