Driving the Speed Limit

[Mike]

I think my answer is off by a bit.

Total energy = 1/2 x Mass x (Velocity)^2

Since the two vehicles are identical, they have the same mass, so we can eliminate the "1/2 x Mass" portion of the formula, since those cancel out.

Technically, we should convert velocity to m/s, but it doesn't really matter, because the proportions will be the same no matter the units.

Therefore, the proportional energy of the two vehicles before they start braking will be 4900 and 6400. The slower vehicle brakes all the way to 0, so it has removed 4900 (units) of energy. Removing the same 4900 from the other leaves 1500 (units). The square root of 1500 is about 39 mph.

The flaw in my thinking is that it only works if the vehicles both brake for the same amount of time. But since the one vehicle is moving faster, it will reach the obstacle first and it will crash before the slower vehicle finally comes to a halt. So actually, it doesn't get the same amount of deceleration as the other car and is probably going even faster than I predicted when it crashes.

I'll leave the actual calculations to a real mathematician though.

[FlameBlade]

That's pretty good. I'm convinced. But I got a toddler going around at 90 mph right now. But yes, Potential energy and Kinetic Energy seems to be the way to go.

[Mike]

Hey! A real mathematician!

[Ronster]

[Phoebe]

Before I went to Atlanta I drove about 5 miles under the speed limit with exceeding caution and courtesy. From the fiery forges of Atlanta I emerged ready to drive getaway cars for criminal organizations or spies. I'm still very courteous though.

[poorpete]

Tried to capture a bumper sticker I saw today that was ~

I'm not going to speed up for you,
If you care that much, just pass me.

[Tahlvin]

Yes, I find the more I travel for work, the faster and more aggressive I tend to drive, until I have a nice long stretch without travel again. Midwest-nice won't cut it when you need to get through big city, downtown traffic in LA, DC, Seattle, Atlanta, etc., and need to be somewhere quickly for a meeting. Back when I was on the road 2-3 times per month, my wife pretty much hid her face whenever we were driving in traffic, because the prevailing philosophy was pretty much a good defense being a good offense, etc., and it never let up. Now that I only travel once every few months, I can usually let out the steam on my drive home from the airport, after which I'm back to normal.

[Ronster]

Agreed! A good respite such as snow/ice shutting down roads coupled with my new shift of 4 on and 3 off makes for a different sort of driver and my first day back it takes a bit for me to embrace the dark side. I do enjoy my drive home. I fill it with podcasts and maybe some music.
Funny how setting changes everything.
Conversely, when I am driving out in our rural setting near home my wife asks me why I drive so slowly. I tell her it is to be safe and to make the pleasant time with her and /or our family together in the car last longer. I actually mean it too. If my wife is napping I will drive extra slow and take the long way home so she can get some zzzzzz. On that note, if one of us is napping in the car she will talk to that person at least once every 3 minutes.

btw, less than an inch of fine snow fell and the schools were closed for 3 days. turns out the sunshine only made it into a sheet of glass and the temps were in he single digits at night, so since our roads are never treated unless it is by me scraping them with the tractor we remained icebound for 2 days. I had to teach my daughter how to handle a car if she came across icy patches.

[Phoebe]

We did that here a little while ago. Perfect conditions of "alone with daughter in car at time of night when parking lot empty but lights on, and sheen of icy snow available to spin out vehicle". Amusing: some suspicious person came to investigate what we were doing. It is obvious what we are doing, especially when we trade driver/passenger seats and sit there practicing things like how to use the turn signal with proper timing.