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23
32
3
2
88
39
2
9
TT
mv
mv
PP
T
L
Pm
P
m
§·
==
=
¨¸
©¹
which implies that
9
constant.
8
PT
mL
Differentiating the above equation gives
30
,
dPT
PT dT
+=
or
.
3
T
dT
dP
P
=−
52. According to the problem statement, the power of the car is
2
1
constant.
2
dW
d
dv
v
m
v
dt
dt
dt
=
=
The condition implies
/
dt
mvdv P
=
, which can be integrated to give
2
00
2
T
Tv
T
mv
mvdv
dt
T
=
¡
=
³³
where
T
v
is the speed of the car at
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 Spring '09
 NAJAFZADEH
 mechanics, Power

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