
Hands
On Physics
The Great Bungee Jump
FREE FALL

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) = deltav / deltat
and
v(bar) = deltax / deltat
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 deltav means
the change in velocity during the interval, deltax means the change
in distance during the interval, and deltat means the change in
time, or the time interval.
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