Distance - again!

This is a futile task. No-one who needs to know reads this. Still and all …

This evening’s Toronto Star carries yet-another-story of high-speed driving. The article focuses, as always, on the legal laws of the city/province/country, with total disregard for the laws of physics and mathematics.

Humans make human laws and humans can sometimes get away with breaking human laws.

But humans DISCOVER laws of physics, and humans can NEVER get away with breaking laws of physics.

To his credit, Toronto police Sgt. Tim Burrows does wave his hands about and circle the issue; it is as if he knows it is there, but can’t quite pull the trigger.

Here it is.

You can look all this up in a book; you can do the calculations with elementary school mathematics, using pencil and paper.

The distance a body moves is given by the formula:

S = ½ ut * at^2

You can read that out aloud as “ess equals you tee times a half ay tee squared”

The time taken to brake under steady deceleration is given by the formula:

t = v/a

“Tee equals vee divided by ay”

Since the final velocity is zero, we can set u=0 and disregard the ut term.

Substituting v/a for t in the first equation, we find:

S = (v^2)/2a

In short, the distance traveled while braking is proportional to the SQUARE of the velocity.

And here’s the beauty of it all:

IT MATTERS NOT ONE WHIT whether you are using kilometers per hour, feet per second, or lupin pods per cats meow!

IT MATTERS NOT ONE WHIT whether you are driving a farm tractor or a lamborghwossit. Maserati. Hyundai Excel. Whatever.

Whatever vehicle is in use (car, ship, train etc) for whatever its braking acceleration is, the distance it will travel under braking is directly proportional to the square of the velocity.

Period.

The star article discusses three speeds:

200 km/h - the speed at which the cars were clocked.

70 KM/h - Toronto police Sgt. Tim Burrows quote

50 KM/h - the recommended MAXIMUM speed for the stretch of road.

Those three speeds squared yield 40,000; 4,900; 2,500.

Go on, work it out for yourself on paper, with pencil.

The ratio of those three “velocity squared’s” to the lowest one comes out to 16.00; 1.96; 1.00.

Go on, work it out for yourself on paper, with pencil.

At the speed limit, you are at par with anyone else driving at the speed limit.

At 20 Km/h over the speed limit (and my guess is that Toronto police Sgt. Tim Burrows has seen plenty of that!), it will take you almost twice the distance to stop.

Another way of saying that is that you have only half as much available space around you as have I traveling at 50 km/h.

But at 200 km/h, you have a miserly 1/16 the space available to you.

At times I wonder if idiots would still be idiotic enough to drive a car 16 times as wide as they do now.

The answer is YES! “.

Neither man owned the car they were driving.”. In other words, they really and truly just don’t care.

So why should we?

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