Derive equation for truck slides before stopping

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The discussion revolves around deriving the stopping distance for a truck and a car that slide after braking, given their masses and the coefficient of kinetic friction. The car stops after sliding a distance d, and the goal is to find the distance D the truck slides before stopping, considering M (truck mass) is greater than m (car mass). Participants mention using the work-energy principle to relate stopping distance to mass, initial speed, and friction. The challenge lies in establishing a clear relationship between the stopping distances of both vehicles based on their differing masses. The conversation emphasizes the need for a mathematical approach to connect these variables effectively.
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Homework Statement



A truck of mass M and a car of mass m are traveling at the same speed. Suppose M>m. Now the drivers of both vehicles suddenly apply their brakes and the vehicles slide along the road, which has coefficient of kinetic friction uk. the car stops after sliding a distance d. assuming uk is the same for both vehicle, what is the distance D the truck slides before stopping?

Homework Equations


The Attempt at a Solution



I have drawn the FBD but i do not know how to relate to the stopping distance. The only thing i could think of is work done.
 
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What is the stopping distance d for the car in terms of its mass and initial speed and the coefficient of kinetic friction?
 
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