Maximum kinetic energy for force F=F0*e^(-kx)

[brad sue]

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

 

[Galileo]

Use conservation of energy.

 

[LeonhardEuler]

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.

 

[brad sue]

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.