Scientific formulas

Equations and graphs Scientific formulas

A formula is a rule written with mathematical symbols that shows the relationship between two or more quantities.

Average speed can be shown with a formula involving distance travelled and time taken.

In the 2019 World Athletics Championships in Qatar, the men’s 100 metre sprint final was won in 9.76 seconds.

Qatar is the small country coloured red and circled

As we have the time and the distance we can calculate the average speed because speed is related to time and distance by the formula below.

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

We can use symbols to represent these quantities. If average speed = s, distance = d and time = t then

$S = \frac{D}{T}$

In the 100 metre final, the distance was 100 metres (m) and the time was 9.76 seconds (s). We can apply our formula to calculate the average speed.

$S = \frac{D}{T}$

$S = \frac{100}{9.76}$

It is important that we get the units right. Units are the amount that something is measured in. In our example the distance is measured in meters and time is measured in seconds. As the speed is calculated by dividing distance by time, the units for speed in our calculation are the units for distance divided by the units for time. This is metres (m) divided by seconds (s) or meters per second (m/s or ms^-1).

$S = \frac{100 metres}{9.76 seconds}$

$S = \frac{100m}{9.76s}$

$S = 10.25ms^{-1}$

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