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arellano (aa39398) – Homework 2 – Weathers – (17101)
1
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001
(part 1 oF 2) 10.0 points
The velocity oF a particle moving along the
x
axis varies in time according to the expression
v
(
t
) =
α

β t
2
where
α
= 56
.
3 m
/
s,
β
= 3
.
85 m
/
s
3
, and
t
is
in seconds.
±ind the average acceleration in the time
interval From
t
= 0 to 1
.
77 s.
Correct answer:

6
.
8145 m
/
s
2
.
Explanation:
Let :
α
= 56
.
3 m
/
s
,
β
= 3
.
85 m
/
s
3
,
and
t
f
= 1
.
77 s
.
v
i
=
α

β t
2
i
= 56
.
3 m
/
s

(3
.
85 m
/
s
3
) (0 s)
2
= 56
.
3 m
/
s
,
v
f
=
α

β t
2
f
= 56
.
3 m
/
s

(3
.
85 m
/
s
3
) (1
.
77 s)
2
= 44
.
2383 m
/
s
,
so the average acceleration is
¯
a
=
v
f

v
i
t
f

t
i
=
44
.
2383 m
/
s

56
.
3 m
/
s
1
.
77 s

0 s
=

6
.
8145 m
/
s
2
.
002
(part 2 oF 2) 10.0 points
Determine the acceleration oF the particle at
t
f
= 1
.
77 s.
Correct answer:

13
.
629 m
/
s
2
.
Explanation:
Let :
t
f
= 1
.
77 s
.
Applying calculus, the acceleration is
a
(
t
) =
d v
dt
=
d
dt
(
α

β t
2
)
=

2
β t
=

2 (3
.
85 m
/
s
3
) (1
.
77 s)
=

13
.
629 m
/
s
2
.
003
(part 1 oF 2) 10.0 points
An electron in the cathode ray tube oF a tele
vision set enters a region where it acceler
ates uniFormly From a speed oF 40200 m
/
s to
a speed oF 4
.
72
×
10
6
m
/
s in a distance oF
2
.
44 cm.
What is its acceleration?
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This note was uploaded on 10/31/2010 for the course PHYSICS 1710 taught by Professor Weathers during the Fall '10 term at North Texas.
 Fall '10
 Weathers
 Work

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