The braking distance is the distance that a vehicle travels while
slowing to a complete stop. The braking distance is a function of several
variables. First, the slope (grade) of the roadway will affect the braking
distance. If you are going uphill, gravity assists you in your attempts to stop and
reduces the braking distance. Similarly, gravity works against you when you are
descending and will increase your braking distance. Next, the frictional resistance
between the roadway and your tires can influence your braking distance. If you have
old tires on a wet road, chances are you'll require more distance to stop than if you have
new tires on a dry road. The last parameter that we will consider is your initial
velocity. Obviously, the higher your speed the longer it will take you to stop, given
a constant deceleration.

The equation used to calculate the braking distance is a child of a more general
equation from classical mechanics. The parent equation is given below.

Vf2=Vo2+2ad

Where:

Vf = Final velocity

Vo= Initial velocity

a = Acceleration rate

d = Distance traversed during acceleration

When calculating the braking distance, we assume the final velocity will be
zero. Based on this, the equation can be manipulated to solve for the distance
traversed during braking.

d = -Vo2/(2a)

Notice that the distance will be positive as long as a negative acceleration rate is
used.

The acceleration of a braking vehicle depends on the frictional resistance and the
grade of the road. From our knowledge of the frictional force, we know that the
acceleration due to friction can be calculated by multiplying the coefficient of friction
by the acceleration due to gravity. Similarly, we know from inclined plane problems
that a portion of the car's weight will act in a direction parallel to the surface of the
road. The acceleration due to gravity multiplied by the grade of the road will give
us an estimate of the acceleration caused by the slope of the road.

The final formula for the braking distance is given below. Notice how the
acceleration rate is calculated by multiplying the acceleration due to gravity by the sum
of the coefficient of friction and grade of the road.

d = V2/(2g(f + G))

Where:

d = Braking Distance (ft)

g = Acceleration due to gravity (32.2 ft/sec2)

G = Roadway grade as a percentage; for 2% use 0.02

V = Initial vehicle speed (ft/sec)

f = Coefficient of friction between the tires and the roadway