The rotation of rod oa about o is defined by the relation θ= 0.5e^ -0.8t*sin3πt, where θ and t are expressed in radians and seconds, respectively. collar b slides along the rod so that its distance from o is r= 1 + 2t- 6t^2 + 8t^3, where r and t are expressed in feet and seconds, respectively. when t= 0.5 s, determine
(a) the velocity of the collar
(b) the acceleration of the collar
(c) the acceleration of the collar relative to the rod.