Let the distance travelled by the vehicle before it stops be $d_{s}$. Then, using equation of motion $v^{2}=v_{0}^{2}+2 a x,$ and noting that $v=0,$ we have the stopping distance

$d_{s}=\frac{-v_{0}^{2}}{2 a}$

Thus, the stopping distance is proportional to the square of the inttial velocity. Doubling the iittial 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 $10 \mathrm{m}, 20 \mathrm{m}, 34 \mathrm{m}$ and $50 \mathrm{m}$ corresponding to velocities of $11,15,20 $ and $25 \mathrm{m} / \mathrm{s}$ which are nearly consistent with the above formula.

Stopping distance is an important factor considered in setting speed limits, for example. in school zones.