Home » Posts » A few notes on using formulas

# A few notes on using formulas

Using formulas is part of Maths which can be really useful in real life situations – and when you are using Maths is Science  – and scientists use Maths all the time!

For example  the formula for working out speed* is
s = d/t  where s is the speed, d the distance travelled and t the time taken

So if we know that a car travels 120km in two hours, the speed overall is  120/2 = 60km/h  (Even the unit for speed tells us how to work it out, which is actually how I usually remember it)

Another question we might be asked is – If a car travels at 40km/h for 30 minutes, how far will it travel?

Here we have the speed and the time, and we can plug our numbers into the formula

40 = ? / 0.5  – we can change this to be ? = 20km by multiplying both sides by 0.5 (30 minutes, hence half an hour)

Which is OK, but a bit awkward, especially if we have a lot of similar calculations

So…. the best thing is to re-arrange the formula to the quantity we always want to find is one the left hand side….  and this is where algebra comes in.

s = d/t.  We can rearrange this formula by multiplying both sides by t.  We may not know what t is but it has a value

s [* t] = d/t [* t]  –  so s * t = d

We reverse the formula, so the single letter is on the left.

d = s * t or d = st (because mathematician are sometimes lazy and leave out the multiply sign)

We call this the ‘subject’ of the formula. In fact, thats how you may be asked to do this in an exam – ‘Make s the subject of the forumla’

I will post with more examples tomorrow

*NOTE: As one of my students mentioned last week, we ‘should be using velocity now rather than speed’.  He had a point, but remember, velocity is the measure where direction is important too..  speed is a useful measure if the direction you are traveling is known or somehow less important.