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47. We use the conservation of energy principle. The initial potential energy is
U
i
=
q
2
/4
πε
0
r
1
, the initial kinetic energy is
K
i
= 0, the final potential energy is
U
f
= q
2
/4
πε
0
r
2
,
and the final kinetic energy is
Km
v
f
=
1
2
2
, where
v
is the final speed of the particle.
Conservation of energy yields
q
r
q
r
mv
2
01

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