Hands On Physics

The Great Bungee Jump

The Math of Free Fall

This page shows how the equations of free fall are based on Newton's Second Law. All descriptions of motion start with Newton's Second Law:

F = m*a

This describes the acceleration (a) on an object of mass m when the net force F is applied. In free fall, the only force acting on the object is

F = m*g

where g is the acceleration of gravity, 9.81 meters per second per second. Together, these equations tell us that the acceleration of the object will be a constant:

a = g

Note that m does not appear in this equation. This is why a penny and a feather will fall at the same rate when there is no additional force of friction.

Now that we know the acceleration, the question becomes, how far does it travel? Distance and acceleration are related through velocity using the two kinematics equations:

a(bar) = delta-v / delta-t
v(bar) = delta-x / delta-t

Here (bar) indicates the average over an interval. So, a(bar) is the avarage acceleration and v(bar) is the average velocity over any interval. Delta means "the change in", so delta-v means the change in velocity during the interval, delta-x means the change in distance during the interval, and delta-t means the change in time, or the time interval.

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