Two springs one trolley, find velocity

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The discussion revolves around solving a physics problem involving two springs and a trolley, focusing on the correct application of principles. The original poster's calculations were incorrect due to the use of a kinematic formula for uniformly accelerated motion, which is not applicable since the acceleration changes with displacement. Instead, the solution should rely on energy conservation principles, specifically the elastic potential energy of the springs. Key questions raised include determining the total spring potential energy at equilibrium and when the trolley is displaced. The conversation emphasizes the importance of using the correct equations and concepts in physics problems.
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Homework Statement



Please refer to the image.

My workings= pencil
Answer= pen

Why is my working wrong? What wrong assumptions did I make?

Homework Equations



Hooke's law/Newton's second law/ Elastic potential energy =0.5 kx^2

The Attempt at a Solution


As shown in the image.
 

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You used a kinematic formula for uniformly accelerated motion. That won't apply here, since the acceleration varies with displacement.

Stick to energy conservation.

What is the total spring PE at equilibrium?

What is the total spring PE when the trolley is displaced?
 
Got it, thank you.
 

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