[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]Uniform rectilinear motion is the most boring motion there is. However, things can get much more interesting if the object following that motion is being chased by another object that also moves at a constant speed, but always toward the first one, like a dog chasing a car. The curve generated in this pursuit is originally called the [i]pursuit curve[/i].[br][br]Note that while the pursued object, represented by the blue point [color=#3d85c6][color=#0000ff]M[/color][/color], maintains its uniform rectilinear motion at a constant speed [color=#cc0000][b]vM[/b][/color], the pursuer (orange point [color=#ff7700]N[/color]) changes the direction of its velocity [color=#cc0000][b][b][b]vN[/b][/b][/b][/color] at every instant, so that while its magnitude |[color=#cc0000][b][b][b][b]vN[/b][/b][/b][/b][/color]| is constant, its velocity [i]vector [/i][color=#cc0000][b][b][b][b]vN[/b][/b][/b][/b][/color] is not.[br][br]In the construction, you can vary the magnitude of [color=#cc0000][b][b][b][b]vN[/b][/b][/b][/b][/color], that is, the speed of the pursuer and the initial positions of both.

[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 and N and stop the animation when N and M are close enough[/color][br][color=#0000ff]SetValue(M, M + dt vM)[br]SetValue(N, N + dt vN)[br]StartAnimation(anima, abs(N − M) > (x(Corner(2) − Corner(1))/400))[br][br][/color][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]