Units for Speed

When we talk about speed, we need to put it in context. If I told you I ran at a speed of $5$5 yesterday you don't yet know whether to be impressed or not. 

If I had run $5$5 kilometres an hour, that's an OK walking speed but it's not anywhere near a running speed. If I ran $5$5 metres a second that would be more impressive. Road signs often don't have a unit given, but they are standardised across a country. In most countries it would be in km/h, but in some countries like the United States and Great Britain, it would be in miles per hour instead.

Measurements of speed are a rate. A rate is a ratio between two measurements with different units. This means units of speed are actually two units put together - one unit of distance and one of time. Can you see why this would be? Think about the formula for speed.

To calculate speed you need to use $\text{Speed }=\frac{\text{Distance }}{\text{Time }}$Speed =Distance Time ​

Notice how distance comes before time in the formula? Units of speed are the same, even including the divide sign $\text{/ }$/ . For common units of distance and time we often use the shorthand, so kilometres/hour becomes km/h and metres per second becomes m/s.

What measurement is appropriate?

When considering which measurement of speed is appropriate to use, you need to think about the likely distance that would be travelled and how much time that would probably take.

You can measure speed in any combination of distance and time, but for numbers to really be useful to us we want them to be easy to compare.

Jet fighter speeds

For example, if I told you that a fighter jet travels $681.736$681.736 mm/s it sounds fast, but you would struggle to really understand what that means. You probably know that travelling at $110$110 km/h is fast for a car, so if I tell you a fighter jet can travel at $2454.2496$2454.2496 km/h, you get a much better idea of how fast that really is. Think of useful comparisons to help you choose appropriate units of speed.

When choosing an appropriate unit of speed, you should also consider the size of the numbers.

Hot Dog Eating Competition

In July 2015, Matt Stonie ate $62$62 hot dogs in $10$10 minutes. Sounds like a lot, but $62$62 hot dogs/$10$10 minutes doesn't work as a unit of speed. You could think of it as $372$372 hot dogs/hour, but Matt didn't keep eating for an hour and this number is quite a large amount to think about. Or you could think of this as $0.1033333333333$0.1033333333333 hot dogs/second but that is a very small number that doesn't mean much. When did you last think about how quickly you can eat $0.1$0.1 of a hot dog? It's difficult to know if you would eat faster or slower than that. Instead you can think of this as $6.2$6.2 hot dogs/minute. Now that is definitely faster than I could eat $6$6 hot dogs!

Worked Examples

QUESTION 1

QUESTION 2