What is stopping distance for vehicle ?

Explanation

When brakes are applied to a moving vehicle, the distance it traavels before stopping is called stopping distance.
Suppose, the velocity of moving vehicle is `v_(0).` After applying brakes retardation : -a
Distance covered : `d _(s)` (stopping distance)
Final velocity `:v =0`
In equation` v ^(2) -v _(0) ^(2) = 2ax`
`therefore 0- v _(0) ^(2) = 2 (-a ) (d_(s)) (because v = 0, a =-a , s = d _(s))`
`therefore v _(0) ^(2) = 2ad_(s)`
`therefore d _(s) =(v_(0) ^(2))/(2a)`
Here, a is value of retardation and it is constant. Thus, stopping distance is proporational to square of the initial velocity.
`therefore d_(s) prop v _(0) ^(2)`