A body of mass 2 kg moving on a horiontal surface with speed `v_(i)=1ms^(-1)` enters a rough patch ranging from `x=0.5m` to `x=1.5m.` If the body comes to rest after passing the patch, then find the retarding force on the body.

Explanation

To solve the problem step by step, we will use the work-energy theorem, which states that the work done by all forces acting on an object is equal to the change in its kinetic energy.

### Step 1: Identify the initial conditions
- Mass of the body, \( m = 2 \, \text{kg} \)
- Initial speed, \( v_i = 1 \, \text{m/s} \)
- The body comes to rest after passing through the rough patch.

### Step 2: Calculate the initial kinetic energy
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