Free fall
This activity belongs to the GeoGebra book The Domain of the Time.
This animation simulates real-time free fall motion, ignoring air resistance. The animation doesn't use formulas (neither equations nor differential calculus), it simply performs the necessary variations in the vectors that direct the motion.
A mass, represented by the blue point, falls from the initial position. As Galileo discovered, the fall time doesn't depend on the mass. Here we can observe the fall, both on Earth (without considering air resistance) and on the Moon.
At each moment, the animation changes both the velocity vector v (in red) and the position M of the mass m due to the action of gravity, represented by the vector g (in green).
For this, every time a small amount of time dt passes, by the definition of acceleration, the velocity increases by dt g. It's that simple; just add the following instruction to the script for the slider anima (Newton's 2nd law):
SetValue(v, v + dt g)
Note: You can stop the animation at any time, but if you do, you must press the 
button to update the time counter.
button to update the time counter.
- Note: By measuring time in seconds (s), distance will be measured in meters (m), velocity in m/s, and acceleration in m/s2.
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 on Earth and M' on the Moon
SetValue(v, v + dt g)
SetValue(v', v' + dt g')
SetValue(M, M + dt v)
SetValue(M', M' + dt v')
Author of the activity and GeoGebra construction: Rafael Losada.