Physics 125 Test I
September 29, 1998
Solutions
1. (15 points) Kinematics
The motion of a particle is given by
k
t
z
j
t
y
i
t
x
t
r
ˆ
)
(
ˆ
)
(
ˆ
)
(
)
(
+
+
=
r
where x(t) = 10.0 m
y(t) = 5.0 + 10.0t m
z(t) = 20.0 – 10.0t –5t
2
m
a). (5 points) Find the velocity
V
r
. Use vector notation.
t
dt
dz
dt
dy
dt
dx
0
.
10
0
.
10
0
.
10
0
.
0


=
=
=
k
t
j
V
ˆ
)
0
.
1
(
0
.
10
ˆ
0
.
10
+

=
r
m/s
b). (5 points) Find the acceleration
a
r
. Use vector notation.
k
dt
V
d
ˆ
0
.
10

=
r
m/s
2
c). (5 points) Find the speed (i.e. the absolute magnitude of the
velocity) at t = 3.0 seconds.
s
m
V
V
V
V
V
V
z
y
x
/
2
.
41
ˆ
40
10
2
2
2
2
2
=
+
=
+
+
=
r
r
(2 point off if units missing)
2. (20 points) OneD motion.
A long massless string with three balls (initially at rest) tied to it at
intervals is dropped. (Newton’s Balls). If the first ball is 19.6 cm from
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the ground, the second is 78.4 cm from the ground and the third is
176.0 cm from the ground, find
a). (5 points) the time it takes for the first ball to hit the ground,
h
1
= 19.6 cm
g=980 cm/s
2
g
h
t
gt
h
2
2
1
2
1
=
=
since v = 0 initially
t
1
= 0.2 s
b) (5 points) the time interval between the first and second ball hitting
the ground,
h
2
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 Spring '08
 MUTCHLER
 Physics, Acceleration, Force, Mark McGwire

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