A particle is projected with velocity v 0 along x -axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin i.e. m a = - α x 2 . The distance at which the particle stops:

Step-by-step solution

F = - α x 2 m a = - α x 2 a = - α x 2   m v d v d x = - α m x 2 ∫ v 0 0 v d v = ∫ 0 x - α m x 2 d x v 2 2 v 0 0 = - α m x 3 3 0 x - v 0 2 2 = - α m x 3 3 x = 3 m v 0 2 2 α 1 3