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The rotation of rod OA about O is defined by the relation θ = 0.5e−0.8t sin 3πt, 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 − 6t2 + 8t3, 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.
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