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

Let the distance travelled by the vehicle before it stops be `d_(s)`. Then, using equation of motion `upsilon^(2)=upsilon_(0)^(2)+2 ax`, and noting that `upsilon = 0`, we have the stopping distance
`d_(s)=(-upsilon_(0)^(2))/(2a)`
Thus, the stopping distance is proportional to the square of the initial velocity. Doubling the initial velocity increases the stopping distance by a factor of 4 (for the same deceleration). For the car of a particular make, the braking distance was found to be 10 m, 20 m, 34 m and 50 m corresponding to velocities of 11, 15, 20 and 25 m/s which are nearly consistent with the above formula. Stopping distance is an important factor considered in setting speed limits, for example, in school zones.