Inserting the formulas you found for xman(t) and xbus(t) into the condition xman(tcatch)=xbus(tcatch), you obtain the following: −b+ctcatch=12at2catch, or 12at2catch−ctcatch+b=0. intuitively, the man will not catch the bus unless he is running fast enough. in mathematical terms, there is a constraint on the man's speed c so that the equation above gives a solution for tcatch that is a real positive number. find cmin, the minimum value of c for which the man will catch the bus. express the minimum value for the man's speed in terms of a and b.