Time function of space

The main feature of theuniform movement (MU)and thescalar speedconstant. When any piece of furniture moves with a constant speed, there is no variation in the speed and, as a consequence, thescalar accelerationis null. This statement may seem contradictory when we compare it to our daily experience, as, in everyday life, the engine speeds up to increase the speed of the car. On a climb, for example, the engine will be accelerated so that the car's speed remains constant.

In Physics, we can say that the word acceleration has only one meaning: the variation of speed per unit of time. Thus, with no variation in velocity, there is no acceleration, therefore, when an automobile describes uniform motion, it makes equal displacements at equal time intervals.

As an example, let's consider an automobile that moves at a constant speed of 80 km/h. We can say that, in 1 hour, it will cover 80 km; in 2 hours, it will cover 160 km; and so on, regardless of whether the path is straight or curved.

Uniform movement on a straight path

Based on what was exposed, we can relate the scalar displacement (ΔS) with the constant scalar velocity (v) through the following expression:

ΔS=v.Δt

As the scalar displacement represents the variation of the mobile space, we have:

ΔS = Sf - Si Sf - Si = v. t

If we represent the initial space by S0 (t = 0) and the final space by S, at any instant t, we will obtain:

S=S0+v.t

This expression is called hourly function of uniform movement. Through it, we can to locate, at any moment, a piece of furniture that moves at a constant speed, as long as we know its initial space and speed.


By Domitiano Marques
Graduated in Physics

Source: Brazil School - https://brasilescola.uol.com.br/fisica/funcao-horaria-espaco.htm

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