Running after a bus. acceleration problem

[LearninDaMath]

Homework Statement

someone is late for a job interview and is running at a constant velocity toward a stopped bus, at some distance from the bus, the bus begins accelerating as some low constant rate.

What's the minimum speed the person must run to just catch up with the bus?

Homework Equations

no idea

The Attempt at a Solution

I know if I set both position equations equal to each other and solve for time, i'll have the time at which they are both in the same position.

And I know the speed of the bus when the person catches up is just the constant acceleration formula for velocity as a function of time (the specific time being the time at which they are both in the same position)

But, how would I find the minimum speed? I could use trial and error a million times with the above velocity equation and narrow it down with the same methodology as trying to find an exact value calculus intermediate value theorem problem. but that could take an eternity if there are a lot of decimal places. There should be a more efficient way, right?

 

[ehild]

Set up the equations for both positions, that of bus and person, in terms of time. When the person, running with the unknown constant velocity V, catches the bus the positions are the same. Solve for t. What should be V that you get real and positive solution?

ehild

 

[Pythagorean]

for setting up an equation of motion for each particle, see hyperphysics:

http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html