I want to talk now about relative speed. What's that mean relative speed?

Well, in our example, we talked about the speed we would have to travel if we wanted to go from home to school in ten minutes and the distance was one kilometre: a thousand metres. And we said that we would travel at a speed of a hundred metres per minute.

Well, the question, is a hundred metres per minute, what does that mean? Relative to what?

Well, in this case, relative to the ground. Now, we don't really think about that. We just think the ground is standing still and so we move over it at hundred metres per minute - that's the speed that we're travelling.

But, think about this: think about driving along on a motorway in a car at, let's say, a hundred kilometres per hour relative to the ground. But now think that another car pulls up alongside travelling at exactly a hundred kilometres per hour as well. You could look into that car - that's your friends sat in that car - and you could wave to them. And as long as both cars carry on travelling at a hundred kilometres per hour, then the cars wouldn't move relative to each other. Even in, like, three hours' time, you can still look out the car window and your friends would still be there. You wouldn't have moved relative to each other.

So, when we speak of a speed we always mean a speed relative to something else. In that case, the relative speed of two cars is zero. They're not moving relative to each other.

Now, if you think about that mathematically, what did you do? You said this one's going at a hundred and that one's going at a hundred, and you subtracted the two speeds to get zero.

Let me give you a slightly different example just to make things clear. So, let's imagine that you're travelling at a hundred kilometres per hour in your car and you overtake another car, which is going along at eighty kilometres per hour. You could say, well what's the relative speed of the two cars? You perhaps can just see in your head. The faster car, the one you're in, is pulling away from the slower car at a hundred kilometres per hour minus eighty kilometres per hour, equals twenty kilometres per hour. So, if you overtake someone, then you subtract the speeds.

Let's say now that instead of overtaking, you're passing someone coming down the motorway on the other side travelling at a hundred kilometres per hour. So you're going at a hundred and they're going at a hundred. What's the relative speed now? Well, now you'd add those two speeds up. You'd have a hundred this way plus a hundred that way, is a relative speed of two hundred kilometres per hour.

Now, remember what I said earlier. Think about whether your maths make sense. What would happen if you added them rather than subtracted them? Well, you should just think, if you've got cars flying towards each other on the motorway, then they approach each other very quickly. You'll see that next time you're on the motorway. The other cars on the other side fly past very fast. Very fest relative speed and the speeds.

Whereas, if you overtake someone, next time you do that on the motorway, just have a look. Just have a watch. Because if you look out of your window and you overtake someone, the car you overtake will indeed recede into the distance, but it will do it very, very slowly indeed even though you're both travelling very fast relative to the ground.

It's that lesson again in physics: just always check your maths and see whether it makes sense, but that is what we mean by relative speed.

Let me just give you one example of relative speed which is, I think, quite surprising.

So, let's say I ask you the question 'What speed are you moving now?'. But I'm a bit lazy. I don't say relative to what. If I just say 'What speed are you moving?', you might say 'Well, I'm not moving at all. I'm sat in my house on my chair, watching television'.

Well, you're right in a way. You're right in the sense that you're not moving relative to the Earth. But you are moving relative to something else. For example, the Earth is in orbit around the sun. It's moving very fast in its orbit around the sun, in fact, you are moving now in orbit around the sun at one hundred thousand kilometres per hour. You can't feel it, and the fact that you can't feel it is a very deep property of the universe indeed. It's the property that motivated Einstein, ultimately, to build his theories of relativity and write things down like E=MC2 and think about things like black holes and many exotic phenomena out there in the universe. So, speed is always quoted relative to something and, in fact, there is no meaning to the idea of speed on its own. You really should say what you're moving relative to.