I’d say 71 MPH vs 77 MPH is a good first approximation, esp. for the purposes of illustrating the perils of kinetic energy and inertia, and I’d say yours is a more precise approximation. Given that the result is the same (dead driver in the red car), I don’t think this is a huge concern, but thanks for doing the math.
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Definitely no understanding of physics. (Which is SCARY when you consider all the people given licenses to pilot these vehicles.) You’re absolutely right, people tailgate and they have no concept of the dangerous metal cages they’re operating.
The point made in the video of an expanding (i.e., spacing is non-linear) speedometer was an EXCELLENT idea and all car manufacturers should implement this. Would be a great way to teach people the physics of piling on speed and what it does to your braking time.
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I used to work at a place that was on a short blind hill and coming back from lunch I realized somebody was tailgating but wasn’t sure how to deal with it but my turn came and I did signal and put on my brakes to turn.
The person behind me slammed on their brakes and skidded and the person tailgating that person rear ended them. I didn’t get hit at all and parked in the office parking lot. The person driving the now rear ended car jumped out and started yelling at me for stopping suddenly. I pointed out the hill in a blind corner and that tailgating was foolish. There are a ton of valid reasons to slam on your brakes there (Though I didn’t) such as animal in the road or a person crossing the street. I did explain about stopping distance and why you need to pay attention to that. The security guard did thankfully shoo the person away.
You tailgate and you will probably get in an accident at a higher rate than other people.
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We could poll all the people who drive vehicles in the world and I would be surprised if more than one in a million know what v^2 = 2ax means.
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You don’t need to be able to solve an velocity equation to understand and respect that it’s really damn hard to stop a ton o metal at higher speeds.
Like how you don’t need to understand ohm’s law to have a healthy respect for electric wires.
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In the podunk city where I live, I am always having to deal with this kind of thing (albeit, not on a blind hill, but light traffic where people follow too close). I am either having to miss my turn, and signal to turn at the traffic-lighted intersection up ahead (because the intersection & traffic lights give more cues that more drivers are expected to turn there, so people behind are more primed to slow down), or I turn on my turn signal for the original turn waaaay earlier and slow down gradually, to prime them for this particular situation. I shouldn’t have to constantly be “driving for two”.
I think maybe speed limits are just a little too high, leading to these kind of situations, or again, drivers are not at a high enough skill level to have the knowledge to hang back.
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I always figured they tell people three seconds because most people count wrong: they start with “one” the moment the car in front passes a marker, and so when they get to “three”, they’ve only actually counted two “mississippis”.
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Case in point: my wife’s mother comes from a country where nobody uses a seat belt in the back of their car. When I am driving I insist she wears a seat belt and this often turns into a waiting game, because it pisses her off. I get that she will never know what v^2 is but likewise she will never understand it’s really damn hard to stop a ton o metal at higher speeds. Its just not part of her world view. From her perspective, if the car stops suddenly she will just bounce around a bit in the back, where everything is soft. From my perspective, she will take my head off on her way to the windscreen. No amount of education or persuasion will solve this problem.
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Shouldn’t you be solving for -3 t^2 + 44.7 t - 81.6 = 0 instead of 3 t^2 + 44.7 t - 81.6 = 0 there?
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Not to mention that, assuming equal reaction times for both drivers, the red car will have gotten considerably closer to the tree in the same period of reaction time delay, thus reducing their braking window even further.
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My mom was the same way the seatbelt laws pissed her off and she refused to wear them.
In the 80s my parents got me a junker car that had no seatbelts (Previous owner had cut them out … the mid 80s were an interesting time)
At one point my brakes failed at an intersection and I smashed into another car while doing probably 20ish and I hit the windshield and cracked the glass. I thankfully don’t remember everything leading up to the hit but that helped me understand the forces involved.
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While this is true, it misses the main thrust. The way most people probably think about the problem (and I know I did), is assume (intentionally or not) that both cars decelerate at a constant rate, and the 100mph car loses 70mph of speed in the same distance it takes the 70mph car to, so it would hit the tree at 30mph. And if this were true, your “who needs math” statement would be absolutely correct.
But the main point isn’t just that the faster you go, the longer it takes to stop. Saying so implies an arithmetic rate, where you subtract x mph per second. It’s in fact a geometric progression, where there is an exponent involved. People shouldn’t be doing calculations in their heads while driving, but they should give themselves four times as much space to stop every time they double their speed. It’s just a different scale of estimation, and it’s an important thing to wrap your head around before you get on the road.
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Yes. I’m off to edit my earlier post…
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Insurance often doesn’t give a damn how fast the person in front slammed on their brakes. You rear-end, it’s your fault.
I know someone who was rear-ended at a stoplight when the guy stopped behind her was rear-ended and pushed into her. BOTH other drivers were deemed at fault – even though stopped, they ruled that the middle driver should have left more space in case they suddenly moved forward. She was NOT held at fault because she had done exactly that.
Moral of the story: always leave extra distance regardless of speed – you and your wallet will hurt less.
Sometimes the financial motivation is the only one certain idiots will pay attention to.
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Unfortunately if you do that where I live, another driver will merge into the space ahead of you, leaving you with less headway. So the optimum tactic is to leave less than two seconds of headway, making it more likely you will hold on to 1.5, or whatever.
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The Citroën DS and SM (and possibly others) had stopping distance on the speedometer, but it was all laid out linear for speed, so didn’t intuitively convey stopping distance.
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I paused the video and thought about it for a few minutes. I suck at this type of math so I was trying to solve it without using any numbers.
When you are performing a emergency stop you feel the force on your body, the force that cuts the seatbelt into you, increase gradually. This means the rate of deceleration increases over time. This means most of the deceleration happens in the end. Which means the red driver is fucked. I guesstimated, without calculations, it would be between 50 and 70, so I was still surprised.
Of course it also helped that he told us the answer was surprising, I wouldn’t have thought about it as long otherwise.
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Interesting. That would be trivial to add to the electronic display in our Jetta, but its not one of the options. But it might be misleading. Reaction times and road conditions vary.
I"m not convinced of your reasoning. I’m going with both cars having the same G-force max deceleration, which leads to a nice easy equation for speed as a function of time (linear).
Can you restate that equation just using emoji, please?
