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EXPERIMENT 3. FREE FALL ANALYSIS
so that an object moving in 1dimension with constant acceleration has a displacement of
the form
y
(
t
) =
y
0
+
v
0
t
+
1
2
at
2
Since we have an expectation for the functional form of the measurements of the displacement
versus time, we can use a process called
curve ﬁtting
to determine the parameters of the
function relating the measured quantities. In this case the initial position
y
0
, initial velocity
v
0
and the acceleration
a
are the parameters relating displacement to time. Knowing these
parameters would allow one to calculate the displacement
y
calc
(
t
) at any time and plot a
continuous curve. Because of uncertainty in measurements, however, the measured data
points would not be expected to lie exactly on this curve (although the range they include 
denoted by “error bars” should overlap the plot for 68% of the data).
When given a set of data points one can seek the parameters of the function that provide
the best matching of the calculated values to the measured values. Starting with some
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 Fall '08
 Staff
 Physics, Acceleration

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