Consider a particle moving along the x-axis where x(t) is the position of the particle at time t, x'(t) is its velocity, and x"(t) is its acceleration. A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is given by a(t) = 9 cos(t). At the time t = 0, its position is x = 4. (a) Find the velocity and position functions for the particle. v(t) = x(t) = (b) Find the values of t for which the particle is at rest. (Use k as an arbitrary non-negative integer.) t =