August 31, 2006
Physics for Scientists&Engineers 1
1
Physics for Scientists &
Engineers 1
Engineers 1
Fall Semester 2006
Lecture 7
August 31, 2006
Physics for Scientists&Engineers 1
2
Position, velocity and acceleration vectors
!
Related through derivatives and integrals
( )
( )
( )
( )
( )
x t
dx t
v t
dt
dv t
a t
dt
!
=
!
=
0
0
0
0
( )
( ')
'
( )
( ')
'
( )
t
t
x t
x
v t
dt
v t
v
a t
dt
a t
=
+
!
=
+
!
"
"
August 31, 2006
Physics for Scientists&Engineers 1
3
Summary: Five Kinematical Equations
Summary: Five Kinematical Equations
!
Onedimensional motion
with constant acceleration
:
!
Can solve practically all onedimensional problems
0
2
1
0
0
2
1
0
0
2
0
0
2
2
0
0
( )
( )
[
( )]
( )
( )
2 [ ( )
]
t
t
v t
v
at
x t
x
v t
at
v
v
v t
x t
x
v
t
v t
v
a x t
x
!
!
=
+
=
+
+
=
+
=
+
"
=
"
August 31, 2006
Physics for Scientists&Engineers 1
4
Free Fall
!
Particular motion with constant acceleration in 1 d
•
a =

g,
with
g =
9
.
81 m/s
2
•
Conventional notation: call vertical axis y axis
!
Kinematic equations for this case
0
2
0
0
1
0
0
2
0
0
2
2
0
0
1
2
( )
( )
[ ( )
]
( )
( )
[ ( )
]
2
t
t
v t
v
t
y t
y
v t
t
v
v t
v
y t
y
v
t
v t
v
y t
y
g
g
g
!
!
=
=
+
=
+
"
=
+
"
=
"
"
"
g
y
F
mg
mge
=
=
!
!
!
!
x
y
g
F
ma
mg
ma
g
a
=
!
=
!
=
!
!
Newton’s Second law
Use those for constant
acceleration:
X > y
a > g
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August 31, 2006
Physics for Scientists&Engineers 1
5
Remarks on Free Fall
!
All objects fall at the same rate,
because
a = g
= constant
•
Need to get rid of air resistance
effects to see this
•
Experiment =>
calculation of g
!
In space, there is almost no
gravity
•
Why all objects float around
•
Not net force: constant velocity,
independent of the mass
0
2
0
0
1
0
0
2
0
0
2
2
0
0
1
2
( )
( )
[ ( )
]
( )
( )
[ ( )
]
2
t
t
v t
v
t
y t
y
v t
t
v
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 Spring '08
 Wolf
 Physics, Acceleration, Velocity, Scientists&Engineers, lly

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