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Speed, velocity and acceleration

Gordon Ansell Disquisition, Science 509 words.

I can be a pedant at times. Misplaced, superfluous or omitted apostrophes, for example, have the power to drive me mad. I sometimes have to resist my pedantry in order not to offend — or indeed murder — people. I regularly see an advert in my local buy and sell forum that’s titled “Vehicle’s for sale” and the superfluous apostrophe therein results in me needing much therapy. Psychiatrists are called, straight-jackets are prepared and knives are removed from my kitchen drawer.

It’s not that I’m intolerant of mistakes. We all make them and I certainly make them aplenty, but a public advertisement with “Vehicle’s for sale” crosses the line. I have seen it many times and surely someone must have pointed out the error. I can’t be the only pedant in the world. I admit I haven’t pointed it out myself but, if I got the bit between my teeth on something like that, I’d probably end up with a restraining order. Instead, I just cry for a few hours and consume a box of tranquillisers.

This all brings me to another area of pedantry, although I understand the confusion here and rarely get arrested for correcting people about the matter. I’m talking about the difference between speed and velocity.

Speed is what eggheads call a scalar quantity. That means it has a single value: 60 miles per hour or 100 metres per second, for example.

Velocity is what those same eggheads call a vector quantity. It consists of two components, one of which is speed and the other is direction. So a velocity would be something like 60 miles per hour north or 100 metres per second in the X direction.

The third term that’s sometimes confused is acceleration. Acceleration is a change in velocity. That means if either the speed or the direction component of velocity changes, a thing can be said to be accelerating. A lot of people think acceleration is simply a change of speed, but it’s not. It can be a change of speed alone but it could also be a change of direction alone.

In a car, for example, you always accelerate around a corner even if you don’t touch the throttle and remain at the same speed. This is because your direction — the other component of velocity — is changing. It is perhaps best not to press this point with the police if you have an accident, though. If you say, quite correctly, that you were accelerating around the corner, the chances are they’d assume you were increasing your speed. Pedantry is not worth a ticket for dangerous driving. Maybe.

You can feel an acceleration. When you accelerate in a straight line by increasing your speed, you are pushed back in your seat. But if you keep your speed constant and turn a corner, you nevertheless feel it — you are pushed to the side.

So, in summary, velocity is not the same as speed. And acceleration is a change of velocity, which may mean a change in speed but it could also merely mean a change in direction.