If the coefficient of friction between the tyres of a car and the road is `mu_(k)`, show that the maximum stopping distance of the car when moving with a velocity v is `v^(2)//2mu_(k)g`

Explanation

To solve the problem, we need to derive the maximum stopping distance of a car when it is moving with a velocity \( v \) and the coefficient of friction between the tires and the road is \( \mu_k \).

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Car**:
- The car experiences a normal force \( N \) acting upwards and the weight \( W = mg \) acting downwards, where \( m \) is the mass of the car and \( g \) is the acceleration due to gravity.
- The frictional force \( F_f \) that acts to stop the car is given by:
\[
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