We'll start with the relative velocity. Let us assume that you are familiar with both terms. They are really not very unusual. The opposite of 'relative' would be 'absolute'. Is there such a velocity at all? After all, the earth also rotates, so that all movement probably takes place at a combined velocity. But we want to neglig the rotation of the earth in the following.

You may have already noticed that the relative velocity is made up of two components. Often a moving train is taken as an example, e.g. letting a person go from the rear to the front of the train. So the speed of walking is added to the speed of the train. Nevertheless, it is time to follow a reference system. With the person in the train, we can therefore be guided by a relative velocity in relation to the ground or rails.

If however train would be much wider and empty inside, one could also move diagonal within wagon. Then in addition the direction should be considered. Both short arrows above show the movement of the human being relative to the car floor and that of the train relative to the rails at the same time. The long arrow adds the two velocities for the direction of movement.

The arrows are thus able to indicate both the pure magnitude of the velocity, and its direction. And as you can see, they even clarify the effect of two simultaneously acting of speed. They can therefore be added together. They are called vectors. The Latin means something like 'leading to a point'.

Now, of course, the need to calculate the speed of people's moving in a train is limited. By the way, this is going to be exciting again when we get to the challenges of of Einstein's teachings. But for now we stay with classical physics with an example a little closer to automotive practice.

Imagine an SUV in a very hilly forest. There is enough space between the trees. But they are also needed for another reason, there, where four-wheel drive is running out of breath. You have already guessed: a winch is being used. So that the example fits here, no tree may be exactly in the preferred direction of movement of the stranded vehicle.

So in order to keep exactly the way up the slope between the trees, our rope wraps around two of them, hopefully with small wooden boards or something similar towards the bark. Now the winch may be able to pull off the car. What can't be seen here: The ropes should be attached to the trees as high as possible, if they are strong enough to lift the car slightly in front and help it over the elevation.

Here once again the situation somewhat simplified, in order to be able to draw in the ruling forces. One could be determined relatively easily, namely the one applied by the electric motor to the wire rope hoist. The length of these should be a measure for this. You can perhaps imagine that the forces to the two trees in the sum are bigger.

This time they are force vectors, but again they are displaceable like all of them. First we moved the upper horizontal a little bit to the right. And now the directions of the two ropes allow us to move the determination of forces to the trees. So you may shift force vectors and not only in the direction of their axis.

It is now also clear that the sum of the forces to the two trees is bigger in amount than that to the car. Which you can't see quite so well: The one closer to the middle of the pulling direction arranged upper tree has to endure a little more. Move it thought down and look at the changes in the force diagram, then you will see it.

Actually, it is an incomplete parallelogram, because you can draw the two force vectors for the trees above the horizontal axis again. Then the vector towards the vehicle would be one of the two diagonals. The one from the starting point of the vectors to the final point in this case of two of them is called the resultant.

You could also use the dashed line to calculate the magnitude of the two forces. Because the two amounts correspond to the lengths of the vectors. Together with the dashed line you get two right-angled triangles. From cosine = adjacent / hypothenuse follows:

Hypothenuse (part left) = amount vector lower tree / cosine of the angle.
Hypothenuse (part right) = magnitude vector upper tree / cosine of angle.

The two parts of the hypothenuse add up to the amount of the vector directed to the car. Forces are something like the salt in the soup of mechanics. One has not only here extraordinarily, Isaac Newton (1642 - 1726). Wikipedia describes him as one of the most important scientists of all time. When his name has become the unity for the force, that may have become also shed some light on its importance.

With what we have learned so far, we can already understand Newton's First Axiom, also called the law of inertia. It emphasizes that a body either remains at rest, or its orbit can be of constant speed, if no 'resulting external forces' occur. If no other force is added to the force that may have pushed it once.

This could then also be air resistance or friction, which Newton excludes with this theorem. You probably know the experiment in which a heavy body in an airless space takes the same time to fall a certain height a feather. It will be exciting to persue the correlation between a moving mass, its acceleration and the force acting on it.