# Scalar Kinematics

Although they often go unnoticed, physical phenomena are always present in our daily lives. We could even say that Physics appears, in one form or another, in all human activities.

**Referential**

We can say that referential is the body in relation to which we identify the state of rest or movement of a piece of furniture. Thus, we say that a mobile is moving in relation to a given reference frame if its position changes, with the passage of time, in relation to it.

**space of a mobile**

To locate a mobile along a trajectory, we must orient it and adopt a point as the origin. The measurement from the point of origin to any point is called space S.

**Variation of space**

Let’s consider a piece of furniture that starts from city A and is located at km 235 of a highway. The mobile takes about 4 hours to reach city B, which is located at Km 672 of the same highway. We call space variation the difference between the arrival space and the output space.

Where:

* ΔS* is the variation of the space

*is the space of departure of the mobile*

**Si***is the space of arrival of the mobile*

**Sf****Average scalar speed**

In automobile races it is common to hear the quote of the “average speed” of a car in a certain lap. We can define the average speed (Vm) of a mobile through the relationship between the variation of space ΔS and the time interval Δt. So we have:

**Instantaneous speed**

We can understand the instantaneous speed (V) as being the average speed for an extremely small time interval, that is, time tending to zero.

**Average scalar acceleration**

We can relate the term acceleration to the variation of the speed of a mobile over time. Thus, we can define the average scalar acceleration αm of a mobile as follows:

**Instantaneous scalar acceleration**

We can understand the instantaneous scalar acceleration as being an average scalar acceleration for a very small time, which tends to zero. Thus, we can define instantaneous scalar acceleration to be: