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 follow these steps:

### Step 1: Understand the Variables
- Let \( v_0 \) be the initial velocity of the vehicle.
- Let \( v \) be the final velocity of the vehicle when it stops, which is \( 0 \) m/s.
- Let \( a \) be the deceleration (braking capacity), which will be a positive value, but we will consider it as negative in our equations since it opposes the motion.
- Let \( s \) be the stopping distance.

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