How Fast Is Fast?

Rafi runs 100 metres in 20 seconds. Nusrat cycles a whole kilometre in 4 minutes.

Who's faster?

Most people answer straight away, and most people get it wrong. Nusrat covered ten times the distance, so surely she's quicker? Read on — she isn't. And the reason she isn't is the whole of this lesson.

The trouble is that neither number means anything on its own. "100 metres" tells you nothing about speed. Neither does "20 seconds." Speed only appears when you put the two together, and that's a genuinely new idea: a measurement made out of two other measurements.

By the end of this lesson you'll be able to:

• explain what speed actually is, in terms of distance and time
• work out a speed from any distance and any time
• read a unit like m/s and say out loud what it means
• compare two speeds properly, even when their units don't match

Speed is a comparison, not a thing

Here's the idea in one line:

Speed tells you how much distance you cover for every one unit of time.

That's all. To find it, you divide:

$\text{speed} = \frac{\text{distance}}{\text{time}}$

Rafi ran 100 m in 20 s. Divide: $100 \div 20 = 5$. His speed is 5 m/s.

Now say that unit out loud the way it's actually written: metres per second. Per means "for every one." So 5 m/s means 5 metres for every one second. If Rafi keeps that up, then in 1 second he moves 5 m, in 2 seconds 10 m, in 10 seconds 50 m.

This is why the unit matters so much here. In the last three lessons a unit was a label stuck on the end of a number. This one is different — m/s is a recipe. It tells you exactly what was divided by what, and if you ever forget the formula, the unit will remind you: metres per second means metres divided by seconds.

One thing speed does not care about is direction. A boy running north at 5 m/s and a boy running south at 5 m/s have exactly the same speed. (Direction does matter for a related quantity you'll meet in a couple of years — many people call it বেগ — but not for speed, and not yet.)