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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:
$ \displaystyle e = m v^2 $Where:
A practical embodiment of this equation that takes into account a typical driver's reaction time, is:
$ \displaystyle d = 1.5 \frac{5280}{3600} v + \frac{v^2}{20} $Where:
A concise version of the above equation, with the absolute minimum number of terms, is:
$ \displaystyle d = 2.2 v + \frac{v^2}{20} $
This equation measures real-world distances, thus it uses field measurements, which will differ to some extent based on their source. 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 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 | Vehicle 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 |
90 | 198 | 405 | 603 |
100 | 220 | 500 | 720 |
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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