If the force acting on a body is inversely proportional to its speed, then its kinetic energy is

Options

A. linearly related to time
B. inversely proportional to time
C. inversely proportional to the square of time
D. a constant

Answer

A

Explanation

`Fprop1/v,F=C/v`
Where C is a constant of proportionality.
`implies ma=C/v " or" m(dv)/(dt)=C/v`
`vdv=(Cdt)/m`
Integrating both sides , we get
`v^2/2 =(Ct)/m "or" 1/2 mv^2=Ct`
or Kinetic energy, `K=1/2 mv^2=Ct "or" K prop t`