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 initial velocity `(upsilon_(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 `upsilon_(0)` and a.

Explanation

Suppose, vehicle stops after covering `d_(s)` distance when brakes are applied. Its initial velocity is `v_(0)`
From equation `v ^(2) - v _(0) ^(2) = 2ax, v = 0 , v _(0) = v _(0), a =- a and x = d _(s)`
`therefore 0- v _(0) ^(2) =- 2a d _(s)`
` therefore d _(s) = (v_(0) ^(2))/(2a) `
Note: Stopping distance is directly proporational to the square of the initial speed of vehicle.
If the speed of the vehicle is doubled, then stopping distance will become four times for given retardation.