Friday, June 06, 2014

Remembering Maths!

I used to love maths at school. Solving equations and doing all sorts of algebra was really interesting. At least it was to me. I can't honestly remember doing a lot of maths when I was working, even though I was involved in research. I guess it was always there in the background. It must have been part of what I did because I was working out equations for curves and for computer models.

I mention this because the other day I wanted to work out an equation for the standard stopping distances given in the highway code. I was reading an article about speeding and wanted to calculate the stopping distance at a particular speed. According to the article, a driver had been caught doing 149mph on the M25 and another doing over 90mph in a 30mph zone.

Anyway, I took the data and worked out an equation. It's written down somewhere, but it was something like:

total stopping distance {in feet} = 0.05(speed{in mph} squared) + speed

Of course in reality it's more complicated, but these are "rule of thumb" numbers anyway. The point is that when you stick in 150mph, the stopping distance is over 1200ft. That's further than a pro golfer's best drive!

What I haven't tried yet is to calculate the deceleration of a standard car over the stopping distances. I'd need some more data and more time on my hands to play with the maths. At a guess I'd say the deceleration will be a curve rather than a straight line. I remember seeing a video of a car braking from 90mph. After 315ft, the standard stopping distance at 70, the car doing 90 had only slowed to 70mph. Scary!

Which brought me to the final bit of maths trivia for the day. A number of years ago I got asked by a nephew this question:

At what temperature is the temperature in Fahrenheit the same as the temperature in Celsius?

I happen the know the answer, but I wanted to remind myself of the maths behind it. Here's how I worked it out.

C = (F-32)*5/9

When C=F

F = (F-32)*5/9

9F = 5F -160

F = -40

Therefore C = F at -40 degrees on both scales.

It might not be very impressive, but at least it kept me amused for a little while the other afternoon. And it's nice to know that not everything I studied all those years ago has disappeared out of my brain!