Why the speed never negative?

Answer 1

Short answer: Because it doesn't have a direction.

Medium answer: Speed can't because it doesn't have direction - whichever direction it's going in, it's going forward. Velocity, on the other hand, can be negative because it does have direction - if it's negative, it's going backwards.

Long answer: (and it's very long. Bear with me here.)

In mechanics, which is the area of math we're dealing with, there are two types of quantities: vector and scalar. Vectors have magnitude (size) and direction; scalars just have direction.

For example, imagine a brick. The brick is quite heavy, and we can describe its heaviness in two ways. We can say that it has a large mass, or we can say that it has a large weight. Mass is a scalar: it doesn't change. If you throw the brick at a wall, it's going to make more or less the same impression as if you throw it at the floor, and no matter which direction you pull it in or where you put it, it always has the same mass.

Weight, on the other hand, is a vector: it has a specific direction - down, or more accurately, the center of the Earth. If you moved the brick 20 miles straight up, it's going to weigh less than if you moved it 20 miles straight down (not very much less, but still). The fact remains that weight always acts down.

The equivalent of the mass/weight difference in the situation we're talking about is speed and velocity. Velocity is a vector - it has a direction and is assumed to always act in that direction. Therefore, if it's negative, it is acting against that direction and moving backwards. Speed is a scalar - like I said before, it doesn't have a direction, so wherever it's going is forward.