Why does doubling your speed quadruple the crash, not double it? A 2011 physics thread still nails it
Kinetic energy scales with v², and the most intuitive explanation isn't an equation — it's two cars braking. Double the speed and you don't just go twice as fast, you also cover more ground while you bleed it off. Both effects multiply.
The work-distance argument carries it: force times distance equals energy, and a faster object travels farther under the same braking force, so the energy isn't 2x but 4x. A reader's two-cars puzzle turns it into a gut-level result.
The thread also surfaces the honest discomfort — one accomplished programmer admits physics' ‘obvious’ cause-and-effect steps have never clicked for him, and asks if he's alone. He isn't.
The intuition behind v²
The 2011 Physics Stack Exchange question keeps resurfacing because the quadratic feels wrong until you see why. The cleanest derivation in the thread is the textbook chain, spelled out by one reader: force equals mass times acceleration, work equals force times distance, and v² = 2ad, which combine to W = ½mv². “This explains why car crashes can be so dramatic, as a doubling of speed results in 4x the kinetic energy.” The reason the distance matters: double your speed and, as one commenter put it, “you are also going to be going twice as far in the same time, not just twice as fast — and they both have the effect of work.”
The two-car puzzle that makes it visceral
The standout contribution was a thought experiment. A reader set up a blue car at 70 and an identical red car at 100, both slamming the brakes at the same deceleration when an obstacle appears. The blue car stops just in time. The red car can't — and the surprising answer, from ½mv², is that it's still doing roughly 71 when it hits, because the blue car's stopping distance only bled off the energy of 70 units of speed, leaving almost all of the red car's extra energy intact. The everyday version came from a woodcutter: it's why a fast, light axe out-splits a heavy maul, and why “you don't see framers using 3 lb hammers” — you can double a light tool's speed, never a heavy one's.
The quiet confession in the replies
What made the thread more than a homework answer was one accomplished developer's admission: he can read and publish papers in math and CS, yet “most cause → consequence” steps in physics demonstrations “make no sense” to him — “Am I the only one?” The replies said no, and pointed him to the books that explain why the math is shaped the way it is rather than just asserting it. For a question first asked fifteen years ago, the most useful thing in the thread turned out to be permission to find it hard.
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