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29. (a) As the body moves along the
x
axis from
x
i
= 3.0 m to
x
f
= 4.0 m the work done by
the force is
22
2
2
6
3(
)
3 (4.0
3.0 )
21 J.
ff
ii
xx
xf
i
WF
d
x
x
d
x
==
−
=
−
−
=
−
−
=
−
³³
According to the workkinetic energy theorem, this gives the change in the kinetic energy:
WKm
v
v
fi
−
Δ
1
2
di
where
v
i
is the initial velocity (at
x
i
) and
v
f
is the final velocity (at
x
f
). The theorem yields
(
2
1
J
)
(8.0 m/s)
6.6 m/s.
2.0 kg
W
vv
m
−
=+
=
+
=
(b) The velocity of the particle is
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 Spring '08
 Any
 Physics, Energy, Force, Kinetic Energy, Work

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