In maths and physics, there are two types of measurements called ‘scalars’ and ‘vectors’. A scalar quantity is simply a number that can increase or decrease. A vector is a number that can increase or decrease, but that also has a direction.
The speed of a car – 20 kilometres per hour, or km/h, for example – is a scalar quantity, meaning it can only go up or down. However, the ‘velocity’ of a car is a vector. This is because velocity is speed in a particular direction – say, 20 km/h south.
A Plane’s Progress
If a plane were to fly from London to Los Angeles – a distance of about 8,800 kilometres – in 10 hours, at what velocity would it need to fly? Logically, you might think it should be 880 km/h west, but what if the wind was blowing towards it at 100 km/h?
Flying into a wind slows things down, so to make the calculation you need to subtract the wind velocity from the plane velocity:
880 – 100 = 780 km/h west.
That’s also why a plane can sometimes arrive sooner than expected – if the wind is behind it, the velocity increases.
Much of the early work related to motion was carried out 400 years ago by the Italian scientist Galileo Galilei. In many ways, Galileo was the first true scientist in that he tried to explain the Universe and the laws that describe what happens in it with the aid of numbers.
The Law Of Falling Bodies
Galileo realized that Earth’s gravity pulls everything downwards, which is why, if things are free to move, they will fall. As they do, the Earth keeps pulling, making them go faster and faster.
One of Galileo’s real strokes of genius was to realize that the presence of air on Earth affects the way things move. In reality, falling objects reach a steady velocity after a while, called terminal velocity. This is because the drag of the air on them stops them speeding up any further, which is why feathers fall more slowly than cannonballs. If you were to drop a feather and a cannonball on the Moon, where there is no air, they would fall at the same rate.
By imagining how things would fall if there were no air, Galileo recognized that the laws of falling objects were very simple. He realized that they could be described with some quite straightforward mathematics:
Objects fall with a steady, or ‘constant’ acceleration. So, if an object is falling at a particular velocity, after 1 second it will be falling twice as fast; after 2 seconds, 3 times as fast; after 3 seconds, 4 times as fast, and so on.
What’s more:
If an object has fallen through a particular distance in 1 second, it will have fallen through a total of 4 times that distance after 2 seconds, 9 times the distance after 3 seconds and 16 times the distance after 4 seconds.
Have you noticed how the two sets of numbers are related? The distances – 1, 4, 9 and 16 – are the squares of the times – 1, 2, 3 and 4. The longer an object falls, the faster it travels.
Did You Know?
You might wonder what the point of these ideas and discoveries is if air resistance means they don’t apply. Well, on Earth, adjustments can be made to mathematical equations to take this into account. And if you travelled into space, you’d soon find them useful – spacecraft obey these rules because there is no air to slow them down.
