lim (kl9356) – Homework 9 – Weathers – (17104)
1
This printout should have 10 questions.
Multiplechoice questions may continue on
the next column or page – fnd all choices
beFore answering.
001
10.0 points
A timevarying net Force acting on a 2
.
5 kg
particle causes the object to have a displace
ment given by
x
=
a
+
b t
+
d t
2
+
e t
3
,
where
a
= 2
.
2 m
,
b
= 3
.
1 m
/
s
,
d
=

4
.
4 m
/
s
2
,
and
e
= 2 m
/
s
3
,
with
x
in meters and
t
in seconds.
±ind the work done on the particle in the
frst 2
.
5 s oF motion.
Correct answer: 420
.
437 J.
Explanation:
Since the Force is time dependent
W
≡
i
x
f
x
i
v
F
·
dvx
=
i
x
f
x
i
ma dx
=
m
i
x
f
x
i
dV
dt
dx
=
m
i
x
f
x
i
dx
dx
dt
dx
=
m
i
v
f
v
i
V dV
=
1
2
mV
2
f

1
2
2
i
.
ThereFore work done on the particle is the
change in kinetic energy. ±or this case,
W
= Δ
K
=
K
f

K
i
=
1
2
m
(
V
2
f

V
2
i
)
,
where the velocity is Found by di²erentiating
the displacement:
V
=
dt
=
b
+ 2
dt
+ 3
et
2
V
i
= 3
.
1 m
/
s
,
and
(1)
V
f
= (3
.
1 m
/
s) + 2 (

4
.
4 m
/
s
2
) (2
.
5 s)
+3 (2 m
/
s
3
) (2
.
5 s)
2
= 18
.
6 m
/
s
,
(2)
where
t
i
= 0 s and
t
f
= 2
.
5 s
.
Evaluation oF the velocity at the initial and
fnal times gives the desired result.
W
=
K
f

K
i
=
1
2
m
(
V
2
f

V
2
i
)
=
1
2
(2
.
5 kg)
b
(18
.
6 m
/
s)
2

(3
.
1 m
/
s)
2
B
= (432
.
45 J)

(12
.
0125 J)
=
420
.
437 J
.
002
(part 1 oF 3) 10.0 points
A 1850 kg car accelerates uniFormly From rest
to a speed oF 11
.
4 m
/
s in 3
.
25 s.
±ind the work done by the net Force on the
car during this time interval
Correct answer: 1
.
20213
×
10
5
J.
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 Fall '08
 Weathers
 Magnetism, Energy, Force, Work, lim, Correct Answer, m/s

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