Question: if it takes 20 feet to stop a car going 20 MPH, how far does it take to stop a car going 40 MPH?
10 feet.
20 feet.
40 feet.
80 feet.
The answer, which surprises nearly everyone, is (4) 80 feet (neglecting the driver's reaction time). This is because the energy of a moving car is
proportional to its mass times the square of its velocity, or:
A practical embodiment of this equation that takes into account a typical driver's reaction time, is:
This equation measures real-world distances, thus it has (ugh) actual numbers in it. It predicts stopping distance in feet for a given velocity in miles
per hour. A reaction time of 1.5 seconds is allowed for the driver to commence stopping (Hey! I didn't invent the car radio!). The factor 5280/3600
simply converts the distanced traveled while reacting into feet per second. Here is a table of typical values, which were generated using this equation
and which agree closely with data published by public safety organizations:
Speed MPH
Reaction Distance Feet
Stopping Distance Feet
Total Distance Feet
20
44
20
64
30
66
45
111
40
88
80
168
50
110
125
235
60
132
180
312
70
154
245
399
80
176
320
496
Virtually no one realizes that a car's stopping distance increases as the square of velocity. Ordinarily, not knowing physics and math is inconvenient.
But in this case it can get you killed.
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The Mathematics Behind Stopping a Car
A practical embodiment of this equation that takes into account a typical driver's reaction time, is:
This equation measures real-world distances, thus it has (ugh) actual numbers in it. It predicts stopping distance in feet for a given velocity in miles
per hour. A reaction time of 1.5 seconds is allowed for the driver to commence stopping (Hey! I didn't invent the car radio!). The factor 5280/3600
simply converts the distanced traveled while reacting into feet per second. Here is a table of typical values, which were generated using this equation
and which agree closely with data published by public safety organizations: