Stopping distance of vehicles : When brakes are applied to a moving vehicle, the distance it travels before stopping is called stopping distance. It is an important factor for road safety and depends on the initialy velocity `(v_(0))` and the braking capacity, or deceleration `-a` that is caused by the braking. Derive an expression for stopping distance of a vehicle in terms of `v_(0)` and `a`.

Explanation

To derive the expression for the stopping distance of a vehicle in terms of its initial velocity \( v_0 \) and deceleration \( -a \), we can use the equations of motion. Here’s a step-by-step solution:

### Step 1: Define the Variables
- Let \( v_0 \) be the initial velocity of the vehicle (before brakes are applied).
- Let \( v \) be the final velocity of the vehicle (after it stops), which is \( 0 \) m/s.
- Let \( a \) be the deceleration (braking acceleration), which is a negative value, hence we can denote it as \( -a \).

### Step 2: Use the Third Equation of Motion
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