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.

A3-mm-thick panel of aluminum alloy (k 177 w/m-k, c 875 j/kg-k and ? = 2770 kg/m) is finished on both sides with an epoxy coating that must be cured at or above t,-150°c for at least 5 min. the production line for the curing operation involves two steps: (1) heating in a large oven with air at ts,0-175°c and a convection coefficient of h, 40 w/m2. k, and (2) cooling in a large chamber with air at 25°c and a con- vection coefficient of he 10 w/m2.k. the heating portion of the process is conducted over a time interval te which exceeds the ime required to reach 150°c by 5 min (h = r + 300 s). the coating has an emissivity of ? = 0.8, and the temperatures of the oven and chamber walls are 175 and 25°c, respectively. if the panel is placed in the oven at an initial temperature of 25°c and removed from the chamber at a safe-to-touch tempera ture of 37°c, what is the total elapsed time for the two-step curing operation?