02prob_11

02prob_11 - Assigment#2 Page 1 of 4 UC Davis Physics 9A...

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Unformatted text preview: Assigment #2, 4/8/11 Page 1 of 4 UC Davis Physics 9A Assignment #2 Cole [2.31]

a)

 a=dv/dt
õ
 The
instantaneous
acceleration
is
the
slope
of
the
 v-t 
graph.

 a(t=3)
=
 0,

 a(t=7) 

=

(45
-
20)(m/s)/(9
-
5)(s)

=

6.25
m/s 2 ,

 a(t=11)
=
 (0
-
45)/(13
-
9)

=

-
11.25
m/s 2 b)

The
displacement
is

 Îx
=
¡
v
dt
=
area
under
v-t
graph.


Îx 1 
=
 (20
m/s)(5
s)

=
100
m Îx 2 

=

(20
m/s)(9
s)
+
 1 2 (25
m/s)(4s)

=
230
m.

 Îx 3 

=

230
m
+
 1 2 (45
m/s)(13
s
-
9
s)

=

320
m. [2.40]

We
are
given
information
on
the
speed
and
distance
but
not
the
time.

We
can
use
the
the
 formula
with
the
time
eliminated.

 v 2 
=
vø 2 
+
2aÎx

õ
 
 v = 0.8 m/s ( ) 2 + 2 1.6 m/s 2 ( ) 5 m ( ) 

=

4.1
m/s [2.75]

a)

The
acceleration
depends
on
time
so
we
must
integrate:

 dv v v ∫ = a dt t ∫ = − 2 + 3 t ( ) dt t ∫ 

 õ
 v = v − 2 t + 3 2 t 2 ,
and
integrate
again
to
find
position:
 dx x x ∫ = v − 2 t + 3 t 2 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ dt t ∫ 
 x − x = v t − t 2 + t 3 2 

õ

At
 t
= 4
s,
 x
=
xø 

õ

 = v − 4 + 4 2 2 

õ

 vø
=

- 4.0
m/s.


 b)
 v = v − 2 t + 3 2 t 2 

õ
 v = − 4 − 8 + 3 2 4 2 =
+12.0
m/s. [2.80]

Set
the
origin
at
the
bottom
of
the
top
of
the
window
with
the
positive
direction
down.

 Then
use
 x = x + v t + 1 2 at 2 

where
 x ø

=

0.

The
flower
pot
falls
through
a
height
 h,
 at
the
top
 of
the
bottom
window:

 h = 1 2 gt 2 .

There
are
two
unknowns
so
we
need
another
equation.

At
the
 bottom
of
the
window:


 h + 1.9 m = 1 2 g t + 0.42 s ( ) 2 

Plugging
the
first
into
the
second
equation
 and
Solving
for
 t: 1 2 gt 2 + 1.9 m = 1 2 g t 2 + 2 0.42 s ( ) t + 0.42 s ( ) 2 ( ) 

õ

 t = 1.9 m 9.8m/s 2 ( ) 0.42 s ( ) − 0.42 s 2 
=
 0.25
s.

õ

 h = 1 2 9.8 m/s 2 ( ) 0.25 ( ) 2 
=
0.31
m. [2.90]

a)

First
find
the
time
the
student
takes
to
hit











b) the
ground.
Position
the
origin
at
the
bottom
with
the
positive
 direction
upwards.

Then,
 y

=
yø
+
vøt
+ 
 1 2 
 at 
2 


where

 yø 
=
180
m, 
vø 
=
0,
and
 a
=

-g 

so
that
 
y 

=
 yø
-
 1 2 gt 2 .

 Solve
for
 t :

 
 t = 2 y − y ( ) g = 2 180 
m ( ) 9.8 
m/s 2 


=

6.06
s.

Superman
has
5
seconds
less
than
this



=

6....
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02prob_11 - Assigment#2 Page 1 of 4 UC Davis Physics 9A...

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