A particle moving along the x axis is acted upon by a single force F = F₀e^-kx, where F₀ and k are constants.The particle is released from rest at x = 0.It will attain a maximum kinetic energy of:

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Quizplus · Accepted Answer

The maximum kinetic energy is obtained by integrating the force over the distance until the force becomes zero. The force given is $F = F_0 e^{-kx}$, where $F_0$ and $k$ are constants. The work done by this force, which equals the maximum kinetic energy (since the particle starts from rest), is found by integrating $F$ with respect to $x$ from 0 to infinity. The integral of $F_0 e^{-kx}$ with respect to $x$ from 0 to infinity is $F_0/k$, which is the maximum kinetic energy the particle will attain.

A Particle Moving Along the X Axis Is Acted Upon