A particle moves in a straight line so that its displacement from a fixed-point O, given by s = 2t + 2 cos 2t, where t is the time in seconds after the motion begins.

a. Find the initial position of the particle.

b. Find an expression for the velocity and the acceleration of the particle in terms of t.

c. Find the time when the particle first comes to rest and its distance from O at this instant.

d. Find the time when the acceleration of the particle is zero for the first time and its distance from O at this instant.