Mechanics

# 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: