# Vector speed

we represent the trajectory ** t** of a particle. In

**scalar kinematics we**determine the position of the particle by its abscissa (or space) S. In

**vector kinematics we**determine the position through its vector . This vector has its origin at a point O (chosen at random) and ends at the point where the particle is.

we represent the positions of the particle at times t _{1} and t _{2} (with t _{2} > t _{1} ). In scalar kinematics we define the space variation Δs by Δs = S _{2} – S _{1} . In vector kinematics we define vector **displacement** in this time interval by:

** = ** ^{_}

That is, the **vector displacement** (or **displacement vector** ) is the vector represented by the oriented segment whose origin is the endpoint of and whose endpoint is the endpoint .

**|∆s| > | |**

When

**|∆s| = | |**

the trajectory is rectilinear or Δs = 0. Thus, in general we have:

** |∆s| ≥ | |**

The average speed is defined by:

The average velocity of a particle is defined by:

As Δt > 0, the values of ** **e must have the same direction and the same sense, as long as **≠ 0 ** . We have seen that, in general, |∆s| ≥ | **| **, thus, dividing by Δt the two members of this inequality, we have:** **