If you want the coat stand to be stable and not tip over, then you really don't want any acceleration to be a factor.
Do a little research on torque (should be in your physics book). If not then http://en.wikipedia.org/wiki/Torque
or other web resources.
If you design the coat stand to be symmetric and perfectly vertical, then the weight of the stand itself will be balanced. The only tipping forces will be what you hang on the coat stand. If you use "hangers" to hold the coats, then their force will be applied to the "hook" or "peg" at something that approximates a point which will result in a downward force. Since the point at which this downward force is applied will not be the center of the coat stand but at some horizontal distance out from the center of the stand, a torque will be applied to the peg or hook which will in turn apply a torque to the vertical coat stand piece. This torque will then be applied to the base which will attempt to tip over the coat stand.
As long as all of the structural members and joints do not bend or deflect enough to matter, this turns into a problem of interacting levers and the problem is to figure out how this translates to a weight balance on the base modeled as a lever.