[color=#0000ff][i][color=#0000ff][i][color=#999999]This activity belongs to the GeoGebra book [url=https://www.geogebra.org/m/mes4bgft]The Domain of the Time[/url].[/color][/i][/color][/i][/color][br][br]After creating a time register, we can place a point [color=#3d85c6][color=#0000ff]M[/color][/color] (representing a mass [i]m[/i]) and create a [b]constant vector[/b] [color=#cc0000][b][b]v[/b][/b][/color]. By the definition of velocity, the mass will move a distance [i]dt[/i] [b][color=#cc0000][color=#0a971e][b][color=#0a971e][b][color=#cc0000][b][b]v[/b][/b][/color][/b][/color][/b][/color][/color][/b]. Therefore, we simply need to add the following instruction to the script of the slider [b]anima [/b](according to [i]Newton's first law[/i]):[br][br] SetValue([color=#3d85c6][color=#0000ff]M[/color][/color], [color=#3d85c6][color=#0000ff]M[/color][/color] + [i]dt[/i] [color=#0a971e][b][color=#cc0000][b][b]v[/b][/b][/color][/b][/color]) [br][br]This instruction ensures that [color=#3d85c6][color=#0000ff]M[/color][/color] moves in a [i]uniform rectilinear motion[/i]. Notice that this instruction only makes [color=#0000ff]M[/color] shift "a little bit" ([i]dt[/i]) in the direction of [b][color=#6aa84f][color=#0a971e][b][color=#0a971e][b][color=#0a971e][b][color=#cc0000][b][b]v[/b][/b][/color][/b][/color][/b][/color][/b][/color][/color][/b] every time the slider's value is updated.[br][list][*]Note: Since the time fraction [i]dt[/i] is measured in seconds, the velocity [color=#c51414][b]v [/b][/color]should be in m/s, and we will use meters as the unit on the axes.[br][/*][/list]To allow [color=#3d85c6][color=#0000ff]M[/color][/color] to return to the initial position [color=#9900ff]P[/color], we can add the following instruction to the script of the [img]https://www.geogebra.org/resource/hwdawgnn/MmhoDfF5M6lNH9D4/material-hwdawgnn.png[/img] button:[br][br] SetValue([color=#3d85c6][color=#0000ff]M[/color][/color], [color=#9900ff]P[/color])[br][br]The uniform rectilinear motion is particularly important because, according to [b]Newton's first law[/b], any mass will remain at rest or continue moving in a straight line at a constant speed (with respect to a reference system) unless acted upon by a net external force. This means that the mass resists any change in its state of motion, a property known as [i]inertia[/i].

[b]SCRIPT FOR SLIDER anima[/b][br][br][color=#cc0000][color=#cc0000]# Calculate the elapsed seconds dt; add one second if t1(1) < tt[/color][/color][br][color=#999999]SetValue(tt, t1(1))[br]SetValue(t1, First(GetTime(), 3))[br]SetValue(dt, (t1(1) < tt) + (t1(1) − tt)/1000)[/color][br][br][color=#cc0000]# Move M[/color][br][color=#0000ff]SetValue(M, M + dt v)[/color][br][br][br][br][color=#999999][color=#999999][color=#0000ff][color=#0000ff][color=#999999][color=#999999]Author of the activity and GeoGebra construction: [/color][/color][/color][color=#0000ff][color=#999999][color=#999999][url=https://www.geogebra.org/u/rafael]Rafael Losada[/url].[/color][/color][/color][/color][/color][/color]