Max distance for person to catch up to bus

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To determine the maximum distance the bus can be ahead of the person while still allowing the person to catch up, one must establish equations for the distances traveled by both the bus and the person over time. The bus accelerates from rest at 2 m/s², while the person runs at a constant speed of 7 m/s. By setting the distance equations equal to each other, the maximum distance can be calculated. The key is to analyze the time it takes for both to cover their respective distances until they meet. Understanding the equations of motion is crucial for solving this problem effectively.
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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...
 
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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.
 

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