94
Chapter 3Acceleration and Free Fall
Summary
Selected Vocabulary
gravity...............................A general term for the phenomenon of attraction between things having
mass. The attraction between our planet and a human-sized object causes
the object to fall.
acceleration.......................The rate of change of velocity; the slope of the tangent line on a v-t graph.
Notation
a........................................acceleration
g........................................the acceleration of objects in free fall
Summary
Galileo showed that when air resistance is negligible all falling bodies have the same motion regardless of
mass. Moreover, their v-t graphs are straight lines. We therefore define a quantity called acceleration as the
slope,
.
v/
.
t, of an objectís v-t graph. In cases other than free fall, the v-t graph may be curved, in which case
the definition is generalized as the slope of a tangent line on the v-t graph. The acceleration of objects in free
fall varies slightly across the surface of the earth, and greatly on other planets.
Positive and negative signs of acceleration are defined according to whether the v-t graph slopes up or
down. This definition has the advantage that a force in a given direction always produces the same sign of
acceleration.
The area under the v-t graph gives
.
x, and analogously the area under the a-t graph gives
.
v.
For motion with constant acceleration, the following three equations hold:
.
x=v
o
.
t+
1
2
a
.
t
2
v
f2
=v
o2
+2a
.
x
a=
.
v
.
t
They are not valid if the acceleration is changing.
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