A particle of mass m=1kg is lying at rest on x-axis, experiences a net force given by law `F=x(3x-2)` Newton, where x is the x-coordinate of the particle in meters. The magnitude of minimum velocity in negative x-direction to be imparted to the particle placed at x=4 meters such that it reaches the origin is `sqrt(P/27) m//s`. find the value of P.

Explanation

The particle is at equilibrium at x=0 and x=2/3

The minimum speed imparted to the particle should be such that it just reaches x=2/3 from there on it shall automatically reach x=0
`1/2 mv^(2)=-int_(4)^(2//3)Fdx=-int_(4)^(2//3)x(3x-2)dx=1300/27` or `v=sqrt(2600/27) m//s`