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

Answer:

F₀ /k .

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 .