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 The Mathematics Behind Stopping a Car

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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?
  1. 10 feet.
  2. 20 feet.
  3. 40 feet.
  4. 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 MPHReaction Distance FeetStopping Distance FeetTotal 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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