A wave on a string is described by `y(x,t)=A cos (kx-omegat)`. (a) Graph `y,v_(y)`, and `a_(y)` as function of x for time t=0. (b) consider the following points on the string: (i) x=0,(ii) x=pi//4k, (iii) x=pi//2k, (iv)x=3pi//4k, (v)x=pi//k, (vi)x=5pi//4k, (vii) x=3pi//2k, (viii) x=7pi//4k`. For a particle at each of these points at t=0, describes in words whether the particle is moving and in what direction, and whether the particle is speeding up, slowing down, or instantaneously not acceleraring.

Explanation

To solve the problem, we will go through the following steps:

### Step 1: Determine the wave function at \( t = 0 \)

Given the wave equation:
\[ y(x, t) = A \cos(kx - \omega t) \]
...