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Stopping Distance

Stopping distance refers to the distance a vehicle will travel from the point 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 road surface, and negligibly by the tires' rolling resistance and vehicle's air drag.

The distance to complete a stop equals the thinking time plus the reaction time times the initial velocity plus the initial velocity squared divided by twice the acceleration of gravity times the coefficient of friction. The time to stop equals the thinking time plus the reaction time plus the initial velocity divided by the acceleration of gravity times the coefficient of friction.

Formula

{QuantityVariable["x", "Distance"] == QuantityVariable[Subscript["t", "r"], "Time"]*QuantityVariable[Subscript["v", "0"], "Speed"] + (Quantity[1/2, "StandardAccelerationOfGravity"^(-1)]*QuantityVariable[Subscript["v", "0"], "Speed"]^2)/QuantityVariable["μ", "Unitless"], QuantityVariable["t", "Time"] == QuantityVariable[Subscript["t", "r"], "Time"] + (Quantity[1, "StandardAccelerationOfGravity"^(-1)]*QuantityVariable[Subscript["v", "0"], "Speed"])/QuantityVariable["μ", "Unitless"]}

symbol description physical quantity
x distance to complete stop "Distance"
tr thinking plus reaction time "Time"
v0 initial velocity "Speed"
μ coefficient of friction "Unitless"
t time to stop "Time"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Stopping Distance"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Stopping Distance"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Stopping Distance"], {QuantityVariable["\[Mu]","Unitless"] -> 1.`, QuantityVariable["x","Distance"] -> Quantity[25, "Meters"]}]
Out[3]=

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