A block of mass m moving with a velocity `v_(0)` on a rough horizontal surface from `x=0` coefficient of friction is given by `mu=mu_(0)+ax`. Find the kinetic energy of the block as function of x before it comes to rest.

Explanation

To find the kinetic energy of a block of mass \( m \) moving with an initial velocity \( v_0 \) on a rough horizontal surface where the coefficient of friction varies with position, we can follow these steps:

### Step 1: Identify the Forces Acting on the Block
The forces acting on the block include:
- The gravitational force \( W = mg \) acting downward.
- The normal force \( N \) acting upward.
- The frictional force \( F_f \) acting opposite to the direction of motion.

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