Speed

Speed measures how far we travel in a unit of time.  This is why we measure it in miles per hour.  Miles measure distance per means in every and hours measure time.  Of course there are other units of speed as well such as kilometres per hour and meters per second which we use a great deal in common entrance physics. Fast and slow moving things might need different units. A rocket will move a certain number of kilometres per second (around 11 km/s to escape earth orbit) a glacier might move a few
centimetres/year. It would be silly to measure these movements in meters per second the numbers would be really big or really small and any calculations you do complicated.
So to measure speed we need to know the distance moved and the time taken. Then we divide the distance by the time. In other words:
Speed= distance / time
If you forget this just think of a speed you go in your car. 50 miles per hour. Miles (distance) per (divided by) hours (time).

I am on a train as I write this we are going 60 miles in 2 hours so the speed is
S=d/t
S=60/2=30 mph

Remember this will be our average speed. We stop at each station, speed up and slow down all the way so we won't go at 30mph exactly much of the time.

If my train was travelling for 4 hours at this average speed how far would it go?
Well the distance=speed x time
Distance =30 x 4 =120 miles.
This is because the speed tells us the distance we go each hour if I go 4 lots of 30 that is 120 miles.
So how long would it take my train to do 105 miles?
Here we do time=distance/speed
Time=105/30=3.5 hours.
Take care. Exam question setters love to put in traps. Look at this question.
A horse travels at 8m/s for two minutes how far does it go?
Here I have muddled up minutes and seconds. The first thing we must work out is how many seconds the horse is travelling for. 2x60=120 (as there are 60 seconds in one minute)
Now we can do
distance=speed x time
Distance=8 x120
Distance=960m

Density

Density
Density measures the mass of cubic centimetre of a material.  This is an important physical measurement for designers, scientists and engineers.  For instance the density of iron is around 7.8 g/cm3 (so a cube one centimetre in all three directions has a mass of 7.8 grams) but the density of Aluminium is only 2.7 g/cm3.  If you replaced all the aluminium parts of an aeroplane with iron it would not get off the ground because the mass of each part would be around three times higher.

Density is also important in predicting if things will float.  A material will float if it is less dense that the liquid or gas it is in.  Water has a density of around 1 g/cm3 (well exactly 1 g/cm3 at 4 degrees centigrade) so materials with a density of less than 1 g/cm3 will float but those with a density of more than 1g/cm3 will sink.  This is also why Helium balloons float, they are less dense than air.

 If you put a helium balloon into a room full of hydrogen what would it do? Well it would sink. Helium is more dense than hydrogen.

Heating and cooling things can change their density.  Hot air balloons work by this principle heating the gases of the air gives the particles more energy so they move apart.  This means there are fewer of them in the same volume of space so compared to the cold air outside the balloon the density drops and the balloon starts to rise.  This is also how convection cells or current work.  Cooling most things makes them smaller so their density rises.  This does not happen with water!  When water freezes it expands and so its density actually goes down which is why icebergs float.

To work out the density of a material  we need to know how to find it mass and volume.  There are different ways to do that shown on these videos:  Density of a rectangular solid<>,  Density of a liquid<>, Density of an irregular solid<>

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