A particle is moving along x-axis under the action of force, F which varies with its position as `F prop(1)/(4sqrtx).` Find the variation of power due to this fore with x.

Explanation

To solve the problem, we need to find the variation of power due to a force \( F \) that varies with position \( x \) as \( F \propto \frac{1}{4\sqrt{x}} \). We will follow these steps:

### Step 1: Express the Force
Given that \( F \propto \frac{1}{4\sqrt{x}} \), we can express this as:
\[ F = k \cdot \frac{1}{4\sqrt{x}} = \frac{k}{4} x^{-1/2} \]
where \( k \) is a proportionality constant.
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