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Physics 231
General University Physics
Spring 2007
Lecture 6
Today
±
Motions in Two Dimensions
²
Projectile Motion
Position and Displacement
±
The position of an
object is described by
its
position vector
,
r
±
The
displacement
of
the object is defined as
the
change in its
position
±
Δ
r
=
r
f

r
i
General Motion Ideas
±
In two or threedimensional kinematics,
everything is the same as as in onedimensional
motion except that we must now use full vector
notation
±
Positive and negative signs are no longer sufficient to
determine the direction
Displacement and Average Velocity in
Motion Diagram
rv
t
ΔΔ
=
GG
Average Velocity
±
The average velocity is the
ratio of the displacement
to the time interval for the
displacement
²
The direction of the average
velocity is the direction of
the displacement vector,
Δ
r
²
Average velocity between
points is
independent
of
path taken (as is the
displacement)
t
Δ
Δ
=
r
v
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Instantaneous Velocity
±
The
instantaneous velocity
is the limit of the
average velocity as
Δ
t
approaches zero
±
The magnitude of the instantaneous velocity
vector is the speed, a
scalar
quantity.
0
lim
t
d
td
t
Δ→
Δ
≡=
Δ
rr
v
Instantaneous Velocity
±
The
direction
of the
instantaneous velocity
vector at any point in a
particle’s path is along a
line
tangent to the path
at that point and
in the
direction of motion
Caution
x
or
y
Average Acceleration
±
The
average acceleration
of a particle as it moves
is defined as the change in the instantaneous
velocity vector divided by the time interval during
which that change occurs.
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 Spring '08
 ELLIS
 Physics, Projectile Motion

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