5
Chap. 2 HW
– part 2
Question
4.
The following equations give the velocity
v(t)
of a particle in four situations:
(a)
v
=
3; (b)
v
=
4
t
2
+ 2
t
 6; (c)
v
=
3
t

4; (d)
v
=
5
t
2

3.
To which of these situations do the equations of Table 21 apply?
The equations of Table 21 assume that
a
= constant (note that this constant can be zero).
Recall that
a
= d
v
/d
t
= d
2
v
/d
2
t.
a)
a
= d
v
/d
t
= 0, so
a
is constant
b)
a
= d
v
/d
t
= 8
t
, so
a
is not constant
c)
a
= d
v
/d
t
= 3, so
a
is constant
d)
a
= d
v
/d
t
= 10t, so
a
is not constant
So the equations of Table 21 apply to a) and c).
5
.
In Fig. 217, a cream tangerine is thrown directly upward past three
evenly spaced windows of equal heights.
Rank the Windows according to
(a) the average speed of the cream tangerine while passing them,
The pie is slowing down so the ranking must be 3, 2, 1.
(b) the time the cream tangerine takes to pass them,
Since it is slowing 1, 2, 3
(c) the magnitude of the acceleration of the cream tangerine while passing them
The accelerations are all the same (=
g
).
All tie.
(d) the change
Δ
ν
first.
Average velocity =
a
Δ
t
So from part b) the ranking is 1, 2, 3
Problems
16.
An electron moving along the
x
axis has a position given by
x
= l6
te
t
where
t
is in seconds.
How far is the electron from the origin when it momentarily stops?
Using the general property
d
dx
bx
b
bx
exp(
)
exp(
)
=
, we write
()
t
t
t
t
t
e
t
te
e
e
dt
d
t
e
t
dt
d
dt
dx
v
−
−
−
−
−
−
=
−
=
⎟
⎠
⎞
⎜
⎝
⎛
+
⎟
⎠
⎞
⎜
⎝
⎛
=
=
1
16
16
16
16
16
This is zero (electron comes to rest) when
t
= 1 s
Then
m
9
.
5
16
=
=
−
t
te
x
19.
The position of a particle moving along the x axis depends on the time according to the
equation
x
=
ct
2

bt
3
,
where
x
is in meters and t in seconds. What are the units of (a) constant
c
and (b) constant
b?
Let their numerical values be 3.0 and 2.0, respectively. (c) At what time does
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 Spring '08
 oshea
 Acceleration, Velocity, Elementary algebra, m/s

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