Kinetic energy of a particle moving in a straight line is proportional to the time t. The magnitude of the force acting on the particle is :

Options

A. Directly proportional to the speed of the particle
B. Directly proportional to `sqrt(t)`
C. Inversely proportional to the speed of the particle
D. Inversely proportional to `sqrt(t)`

Answer

C, D

Explanation

`1/2 mv^2 = kt implies m v (dv)/(dt) = k implies a = k/(mv) implies F = k//v`
`v = sqrt((2 kt)/(m)) , " "F = ma = sqrt((m k)/(2t)) implies F alpha t^(-1//2)`.