First, we assume a spherical car...

Ah, the perfect physics world. It's a fun place to go from time to time.

MechE here, the limiting factor for car accelerations is usually the static coefficient of friction between the car tires and the road, _not_ the power of the brakes or strength of the engine.

Without ABS braking, it is quite easy to "skid" while applying a harsh brake because you overcome the limit of force between the tires and the road. Similarly, it is quite easy to "burnout" as well with a strong engine for the same reason.

So although the strength of the two systems is not the same, the limiting factor for both of them is identical. Hence, symmetry.

The limiting factor on acceleration in the Toyota Yaris is ont the tires.

This is true for the deceleration side of things (nearly any car can lock it's brakes at any speed), but on the acceleration side of the curve, this is typically only true in first, and perhaps second gear. It would take a truly obscene amount of power to smoke the tires while already in 5th gear (assuming you dont "cheat" by popping the clutch).

Obviously burning out in 5th is almost impossible, but I was considering the stop sign case where you are starting from rest in 1st gear.

Car owner here. I don't think this is right.

Yeah, this argument would only apply to all-wheel-drive cars that are powerful enough to burnout on all four wheels.

It actually applies in a few cases:

* All wheel drive cars, with all-wheel braking

* Two-wheel drive cars, with braking systems that are primarily biased towards the front.

Both cases rely on either all four wheels or accel/decel or only two

First comment: "venky said...

He claims in his model, 'his car decelerated at - 10 m/s^2 and, instantaneously, accelerated to + 10 m/s^2 at t = 0'.

No known mechanical system is capable of achieving such an instantaneous jump without a tail-off period. ...."

MechE here, electrical motors can obtain almost instantaneous acceleration / full torque at 0rpm. Their torque curves typically look like this:

http://www.jmag-international.com/catalog/img/e68-3b.gif

The brakes are independent, so it's not as if one system has to provide both accelerations, one just needs exceptional timing of the feet. A lot of rally car drivers can do similar maneuvers

This is the same reason why the Tesla Roadster has such a killer 0-40mph

A modern hatchback (VW Golf) with good tires on a perfect road can decelerate at 1g with a pro driver. In tests regular drivers posted between 0.9 - 0.6g in a range of cars from Ferrari to Honda civic.

To do 1g in acceleration you would need to do 0-60 in 2.75s that MIGHT be possible for a $1M supercar (or a bike ;-)

The Ariel Atom can do that in 2.9 seconds for about $60k USD. On a scatter plot of acceleration vs sticker price, the Atom is a true outlier.

http://m.youtube.com/watch?v=6v4YNkurhLk

The only point on that plot which would be even more of an outlier would be a shifter-kart.

I think a GT-R can do that. It's certainly close.

GT-R is a $1mm supercar that happens to be underpriced at $80k.

Which is what happens when the techniques of lean manufacturing are applied to the supercar design brief. First of this vein was the Honda NSX, I believe.

I have a hunch that the reliability of these cars far exceeds that of the big Italian names...

I belong to a car club that lets you take these out. Supposedly the GT-R eventually disintegrates its own transmission. So did a Ferrari F430. The newer Ferraris don't anymore, supposedly.

IIRC if you use the launch control that explicitly (as in documented in the manual) puts several hundred miles' worth of wear on it - and I'd guess anyone who takes it out in a car club like that will try it at least once (I know I would). Could it just be that?

It depends on the car.

On the 2010 GTR, using it at all voids the launch control. And had automatic ejection from the club, losing your membership. On the 2012 GTR, it doesn't have launch control anymore.

Meanwhile some other cars have launch control which doesn't void the warranty (eg BMW 135i w/ dual clutch. Of course it has half the HP...)

They sold the 2010 at around 50k miles. Similarly a f430's gearbox is only rated for 20k miles.

Do they have Tesla Roadsters?

Wut

I doubt there is any car that can unless the brakes are really dodgy (apart from the rocket powered ones with parachutes)..

Just goes to show, if you haven't got a hope in hell, try bullshit and long words.

[edit] Just looked up formula one cars, they are 2g acceleration and 5g braking apparently.

But then the prosecution would have to bring it's own expert witness...over a traffic ticket.