Box moving on a decelerating truck?

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A physics problem involves a truck decelerating while carrying a wooden box, with the goal of determining the maximum stopping distance before the box hits the cabin. The teacher indicated that the box's acceleration relative to the truck is μkg, while the truck's acceleration is -μkg. There was initial confusion regarding the teacher's reasoning, but it was clarified that the question seeks the maximum distance the truck can travel before the box moves forward. The discussion also revealed a potential mistake in the teacher's solution, prompting further examination of the problem. Overall, the participants are working towards a clearer understanding of the dynamics involved in the scenario.
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Homework Statement


A truck with a steel bed carries a wooden box, where μs = 2μk. The box of mass m is in the middle of the bed of length l. If the truck is moving forward with velocity vo but is slowing down, determine the maximum distance the truck can take to stop before the box hits the cabin of the truck in terms of the variables given.

Homework Equations


F = ma, Fk = μkmg

The Attempt at a Solution



So my teacher said that the acceleration of the box relative to the truck is aB = μkg, while the acceleration of the truck relative to the ground is aT = -μkg. I'm having trouble understanding how my teacher got this... I do know that the acceleration of the block relative to the ground is a = μg, but I don't know how my teacher got the acceleration of the block relative to the truck. Can anyone help clarify my teacher's reasoning?


Any help is appreciated. Thank you so much!

In case you guys want to look at my teacher's actual solution, here it is. My question is about part b): https://dl.dropbox.com/u/12682457/m%20%26%20f%20%232%20copy.jpg
 
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You wrote,

"...determine the maximum distance the truck can take to stop before the box hits the cabin..."

Shouldn't that be the minimum distance the truck can take to stop? If we decelerate slowly the box won't move relative to the truck.

Edit, ignore the above question, it now makes sense to me.
 
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Does this look right?
 

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@Spinnor: Yes, that does look correct to me! :) Except the question is looking for the maximum distance the truck travels :O

I discussed this again with my teacher, and apparently, there might be a mistake in my teacher's work. But yes, thank you for your solution! It gave me an idea of what the correct solution should look like...
 
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