A box of mass 200 kg is kept on a rough horizontal floor having coefficient of static friction `mu_(s)=0.25` and coefficient kinetic friction `mu_(k)=0.2.` Find the work done by a man to slide the body slowly through 20 m with a minimum force. Also find the magnitude of the minimum force.

Explanation

To solve the problem, we need to find the work done by a man to slide a box of mass 200 kg through a distance of 20 m on a rough horizontal floor, along with the magnitude of the minimum force required.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of the box, \( m = 200 \, \text{kg} \)
- Coefficient of static friction, \( \mu_s = 0.25 \)
- Coefficient of kinetic friction, \( \mu_k = 0.2 \)
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