Max distance for person to catch up to bus

[circuscircus]

Homework Statement

THe bus is D=10m ahead of the person and accelerates from rest at a=2m/s^2 while the person runs after it at 7m/s. Suppose D is not specified, what maximum distance can the bus be ahead of the person that will allow the person to catch the bus?

Homework Equations

The Attempt at a Solution

I'm not really sure how to approach this...

 

[mgb_phys]

You need an equation describing the distance the bus has moved with time, and a different equation for the person.
When they catch the bus they have the same distance so set the equations equal,
look in the sticky thread for equations of motion or in your textbook.