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

To solve the problem, we will apply the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.

### Step-by-step Solution:

1. **Identify the Given Information:**
- Mass of the particle, \( m = 1 \, \text{kg} \)
- Initial position, \( x = 4 \, \text{m} \)
- Final position, \( x = 0 \, \text{m} \)
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