After a not$-$so$-$successful exam Joe has gone to a store to buy some comfort. The conveyor belt is moving at what appears to Joe as a snail's pace, so he asks the sales clerk to speed it up$,$ but the clerk says that it has been designed to accelerate slowly in order to keep the groceries unharmed. This leads to Joe thinking the physics of the situation. What would be the largest possible acceleration so that the soon$-$to$-$be his bottle would not tip over or slip at the conveyor? The coefficient of static friction between the belt and bottle is $0\mathrm{.}2.$