Solve Physics 11 Problem: "Did Person Catch Bus?

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The physics problem involves a person running towards a bus that starts moving after a delay. The person has an initial speed of 1.7 m/s and accelerates at 1.3 m/s² for 4 seconds, reaching a maximum speed of 6.9 m/s. Meanwhile, the bus accelerates at 2.6 m/s² from rest. The discussion focuses on how to calculate the distances traveled by both the person and the bus to determine if the person catches the bus. Clarification on creating distance formulas for both the person and the bus is needed to solve the problem effectively.
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Homework help, please! Urgent

This is the question from my physics 11 class, it has completely stumped me, i have done about have the question, i just get stuck when it comes to proving that the persone has or has not caught the bus.

here it is:

A personne walking at a speed of 1.7m/s see's a stopped bus 25m from him. At this moment this person starts to run with an acceleration of 1,3m/s2. After 4 secondes this personne has reached his maximum speed et it stays constant, but at the same time the bus starts moving and accelerates 2,6m/s2.

Does this person suceed in catching the bus? If so, at what time and at what distance, if not what was the smallest distance between the person and the bus.

- I am sorry if there any mistakes, i translated from french.


Ive got this so far:

Alright well, by using the initiale speed of 1,7m/s and 4s, i found his constante speed of 6.9m/s. So after that i used the acceleration and his speed to determine the distance he travelled, 17,2m. i subtracted 17,2m from 25m, which left 7,8m between the bus and the person. Then I am stuck, how do i incorporate both speeds in one equations to see if he caught the bus or not?

Update, i tryed using a time of 8s for both the peron and the bus, and i see that the bus is goin faster then the person and has traveled a dreater distance, the only problem is don't know what has happened between 4s and 8s, I am completely lost:confused:
 
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Welcome to PF, Nick. Please note that you must show your work before we can help with homework questions. How far have you got?
 
To solve such a question:
1. Write a traversed distance formula for the person and one for the bus, both distance formulas as functions of time.

Can you do that?
 
i added my work, to the bottom,
 
reply for travers distance formula thing, my classes are in french and i don't know what that means or we didnt learn that yet
 
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