Speed from Braking Distance

The Speed from Braking Distance calculator estimates the initial speed based on the distance to stop a vehicle (d) and the a braking coefficient (μ).

INSTRUCTIONS: Choose units and enter the following:

• (d) The Braking Distance 
• (μ) The Braking Coefficient 

Speed from Braking Distance (v):  The calculator returns the speed (v) in kilometers per hour.  However this can be automatically converted to other velocity units (e.g. miles per hour) via the pull-down menu.

The Math / Science

The formula for the initial velocity from the breaking distance is:

          `v = sqrt( 2 * mu * g* BD)`

where:

• v = initial velocity
• BD = Breaking Distance
• μ = friction factor
• g = acceleration due to gravity on earth

The Braking distance refers to the distance a vehicle will travel when its brakes are fully applied to when it comes to a complete stop. It is primarily affected by the original speed of the vehicle and the coefficient of friction between the tires and the roads surface, and negligibly by the tires rolling resistance and vehicle's air drag. The type of brake system in use only affects trucks and large mass vehicles, which cannot supply enough force to match the static frictional force. 

The breaking distance is one of two components of total stopping distance. The following formula is used to calculate the braking distance: 

                    `BD=v_i^2/(2mug)`
where:

• BD = Breaking Distance
• v_i  = initial velocity
• μ = friction factor
• g = acceleration due to gravity on earth

Braking Coefficient

The Braking Coefficient is a coefficient of kinetic friction.  For accident reconstruction on dry surfaces, a value of 0.7 is often used.  This is the default value in this calculator.  A modern car with computerized anti-skid brakes may have a friction coefficient of 0.9 - or even far exceed 1.0 with sticky tires. 

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References

Formula and definition are from Wikipedia (https://en.wikipedia.org/wiki/Braking_distance).