A body of mass 2 kg moving on a horizontal surface with a 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 can follow these steps:

### Step 1: Identify the given values
- Mass of the body, \( m = 2 \, \text{kg} \)
- Initial speed, \( v_i = 1 \, \text{m/s} \)
- Final speed after passing the rough patch, \( v_f = 0 \, \text{m/s} \)
- Displacement of the rough patch, \( S = x_2 - x_1 = 1.5 \, \text{m} - 0.5 \, \text{m} = 1 \, \text{m} \)

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