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Freely Falling Bodies
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One Dimensional Motion with
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One Dimensional Motion with
Derivation of Kinematic Equations of Motion
Choose
t
_{i}
0,
x
_{i}
0,
v
_{i}
v
_{0}
, and write
x
_{f}
x
,
v
_{f}
v
and
t
_{f}
t
.
a
=
constant
a
=
. Then Eq.(
2.5
)
a
=
or
v
=
v
_{0}
+
at
(7)
a
=
constant
v
changes uniformly
=
(
v
_{0}
+
v
). From Eq.(
2.1
)
=
x
/
t
. Combining:
x
=
t
=
(
v
_{0}
+
v
)
t
. Using Eq.(
2.7
) we get:
x
=
v
_{0}
t
+
at
^{ 2}
(8)
Eq.(
2.7
)
t
= (
v

v
_{0}
)/
a
. Substitute into Eq.(
2.8
)
x
= (
v
+
v
_{0}
)(
v

v
_{0}
)/(2
a
) or,
v
^{ 2}
=
v
_{0}
^{2}
+ 2
ax
(9)
Note that only two of these equations are independent.
Next:
Freely Falling Bodies
Up:
One Dimensional Motion with
Previous:
One Dimensional Motion with
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10/9/1997