Solving for Maximum Kinetic Energy of a Particle in Motion | F=F0*e-kx

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To find the maximum kinetic energy of a particle influenced by the force F=F0*e-kx, apply the work-energy theorem, which states that the change in kinetic energy equals the net work done on the particle. Starting from rest at x=0, integrate the force over the distance to determine the total work done. The integration limits will help calculate the maximum kinetic energy, which is ultimately expressed as F0/k. Understanding the relationship between force and work is crucial in solving this problem. This approach leads to the conclusion that the maximum kinetic energy attainable is indeed F0/k.
brad sue
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Hi I need help for this problem very quick,please!

A particle moving along the x-axis is acted upon by a single force F=F0*e-kx, where F0 and k are constants. The particle is released from rest at x=0.

What is the maximun kinetic energy it can attain?

The answer is F0/k but I don't know how to get it.
Thanks
B
 
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Use conservation of energy.
 
By the work-energy theorem the change in kinetic energy of a particle is equal to the net work done on it. Over an infinitisimal distance dW=\vec{F}\cdot d\vec{s}. To get the total work, you have to integrate. The particle starts at rest at x=0 and we want to know the highest kinetic energy it could ever reach. You should be able to figure out what limits to integrate over.
 
LeonhardEuler said:
By the work-energy theorem the change in kinetic energy of a particle is equal to the net work done on it. Over an infinitisimal distance dW=\vec{F}\cdot d\vec{s}. To get the total work, you have to integrate. The particle starts at rest at x=0 and we want to know the highest kinetic energy it could ever reach. You should be able to figure out what limits to integrate over.

Thank you very much.
 

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