In a certain machine two steel plates are separated by a hardened steel cylindrical roller (see fig). In operation, the plates move back and forth horizontally, perpendicular to the axis of roller, and the roller rolls freely between plates without slipping on either one. At a particular instant plate A is moving with a speed of 18 cm sec$$^{-1}$$ to the right and an acceleration of 30 cm sec$$^{-2}$$ to the left, and the plate B is moving with a speed of 6 cm sec$$^{-1}$$ to the right and an acceleration of 8 cm sec$$^{-2}$$ to the left. At that instant, for the roller