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

Options

A. constant
B. directly proportional to time
C. inversely proportional to time
D. directly proportional to square of time

Answer

B

Explanation

`F prop 1/v`
`F=lambda/v`, where `lambda` : constant
`ma= m (dv)/(dt)=lambda/v implies m int_(0)^(v) dv =lambda int_(0)^(t) dt`
`m|v^(2)/2|_(0)^(v) =lambda |t|_(0)^(t) implies 1/2 mv^(2)=K=lambda t`
`K prop t`