The $900-$kg motorized unit A is designed to raise

and lower the $600-$kg bucket B of concrete. Deter$-$ mine the average force R which supports unit A during the $6$ seconds required to slow the descent of the bucket from $3$ m$/$s to $0\mathrm{.}5$ m$/$s$.$ Analyze the entire system as a unit without finding the tension in the cable.