Question

A particle is acted upon by a net force F=F0e-kx, where F0 and k are constants. If the particle has velocity equal to zero at x=0, then the maximum kinetic energy that the particle can attain is:_____.

1. F0/k
2. F0/ek
3. kF0
4. (kF0)2
5. kekF0

Answer 1

F₀ /k .

Step-by-step explanation:

Force is variable

F=F₀
`e^(-kx)`

kinetic energy = work done by force

= ∫ F dx

= ∫F₀
`e^(-kx)` dx

= F₀
`e^(-kx)` / -k

E = F₀
`e^(-kx)` / -k

= -F₀ /(k
`e^(kx)` )

For maximum E ,
`e^(kx)` should be minimum ,

`e^(kx)` is minimum for x = 0

maximum value of E = F₀ /k .