A man is running at speed c (much less thanthe speed of light) to catch a bus already at a stop.At t=0, when he is adistance b from the door to the bus, the busstarts moving with the positive acceleration a.
Use a coordinate system with x=0 at the door of thestopped bus.

a)

What is xman(t), the position of the manas a function of time?

Answer symbolically in terms of thevariables b, c,and t.

xman(t) =

b)

What is xbus(t), the position of the busas a function of time?

Answer symbolically in termsof a and t.

xbus =

c)

What condition is necessary for the man to catch the bus? Assumehe catches it at time tcatch.

What condition is necessary for the man to catch the bus? Assumehe catches it at time .

xman(tcatch)>xbus(tcatch)

xman(tcatch)=xbus(tcatch)

xman(tcatch)<xbus(tcatch)

c=a?tcatch

d)

Inserting the formulas you foundfor xman(t) and xbus(t) intothecondition 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 runningfast enough. In mathematical terms, there is a constraint on theman's speed c so that the equation above gives asolution for tcatch that is a real positivenumber.

Find cmin, the minimum valueof c for which the man will catch the bus.

Express the minimum value for the man's speed in termsof a and b.

cmin =