This activity belongs to the GeoGebra book The Domain of the Time. This animation simulates the vertical launch of an object upwards in real time, neglecting air resistance, with a given initial velocity v_y​. The animation does not use formulas (neither equations nor trigonometry nor differential calculus) and only performs the necessary variations in the vectors that direct the motion. Remember that, after using the clock to establish small time intervals (dt), the animation, at each step, essentially uses these two instructions: SetValue(v, v + dt g)  SetValue(M, M + dt v) This means that each time the value of the "anima" slider is updated, the velocity v increases slightly (by dtdtdt) in the direction and sense of g, and M moves slightly in the direction and sense of v. As you can observe, the result fits quite well with reality.

SCRIPT FOR SLIDER anima # Calculate the elapsed seconds dt; add one second if t1(1) < tt SetValue(tt, t1(1)) SetValue(t1, First(GetTime(), 3)) SetValue(dt, (t1(1) < tt) + (t1(1) − tt)/1000) # Move M SetValue(v, v + dt g) SetValue(M, If(y(M + dt v) > 0, M + dt v, (x(M), 0)) StartAnimation(anima, y(M) > 0) Author of the activity and GeoGebra construction: Rafael Losada.