1
Lecture 3
Vectors
Two Dimensional Motion
Relative Motion
Physics 111, Summer 2011, June 15, Lecture 3
Summary
There are four types of motion: horizontal
, vertica
l, circular
, two dimensional
,
and projectile
.
Acceleration tells us how quickly the velocity changes:
the change in velocity divided by the change in time:
t
v
a
Δ
Δ
=
/
gy
y
g
Acceleration from
the rest (
a
= const):
at
v
=
at
v
2
1
=
2
2
1
at
x
=
Acceleration during
the motion (
a
= const):
at
v
v
+
=
0
2
0
at
v
v
+
=
2
0
2
1
at
t
v
x
+
=
If the air resistance can be ignored, any object falls down with a constant
downward acceleration of
g
= 9.8 m/s
2
regardless of its mass and composition.
2
Some equations for vertical
motion (
g
= const):
gt
v
v
+
=
0
2
0
0
2
1
gt
t
v
y
y
+
+
=
Physics 111, Summer 2011, June 15, Lecture 3
♦
A
scalar
is a quantity which has the magnitude
only:
mass, length, time, volume, temperature,
etc
.
Scalars and Vectors
♦
vector
is a quantity which has the magnitude
and direction
:
(Magnitude of
)
A
A
♦
In physics we need
vectors
because the real world is at least
three dimensional
.
displacement, velocity, force,
etc
.
A
A
=
=
3
A
−
B
A
B
A
B
A
⋅
−
+
,
,
Physics 111, Summer 2011, June 15, Lecture 3
♦
How we can show a vector, indicating, for example, the velocity of
30 m/s at 30
0
to northeast?
Vectors: Magnitude and Direction
0
0
1. Magnitude:
choose a scale:
2. Direction:
show the angle of 30
0
to +
x
axis:
s
m
v
/
10
=
s
m
v
/
30
=
)
(
north
y
+
4
0
30
=
θ
A
)
(
south
y
−
)
(
west
x
−
)
(
east
x
+
)
30
,
/
30
(
0
s
m
A
0
Physics 111, Summer 2011, June 15, Lecture 3
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Working with Vectors (#1)
1. Addition
2. Subtraction
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 Summer '08
 B
 Acceleration, Velocity, ax

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