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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`.

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Let the distance travelled by the vehicle before it stops be `d_(s)`. Then, using equation of motion `v^(2) = v_(0)^(2) + 2 ax`, and noting that `v = 0`, we have the stopping distance
`d_(s) = (-v_(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 50m 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.

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