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Physics 1301: Chapter 2, Pg 1
Chapter 3: Motion in 2D and 3D
¾
Position and displacement
¾
Velocity and speed
¾
Acceleration
¾
Trajectories
¾
Motion with constant acceleration
¾
Projectile motion
¾
Uniform circular motion
¾
Relative motion

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*Sign up*Physics 1301: Chapter 2, Pg 2
Position vector
Position vector:
¾
= a vector connecting the origin of
the coordinate system to the point
of interest
¾
2D:
j
i
r
⋅
+
⋅
≡
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
⇒
≡
)
(
)
(
)
(
)
(
)
(
0
t
y
t
x
t
y
t
x
t
z
k
j
i
r
⋅
+
⋅
+
⋅
≡
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
≡
)
(
)
(
)
(
)
(
)
(
)
(
)
(
t
z
t
y
t
x
t
z
t
y
t
x
t

Physics 1301: Chapter 2, Pg 3
Displacement vector
Displacement vector:
¾
= change of position vector:
¾
Vector notation:
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
∆
∆
∆
≡
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
−
∆
+
−
∆
+
−
∆
+
≡
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
−
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
∆
+
∆
+
∆
+
≡
∆
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
t
z
t
y
t
x
t
z
t
t
z
t
y
t
t
y
t
x
t
t
x
t
z
t
y
t
x
t
t
z
t
t
y
t
t
x
t
r
)
(
)
(
)
(
t
t
t
t
r
r
r
−
∆
+
≡
∆
k
j
i
r
⋅
∆
+
⋅
∆
+
⋅
∆
≡
∆
)
(
)
(
)
(
)
(
t
z
t
y
t
x
t

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*Sign up*Physics 1301: Chapter 2, Pg 4
Average velocity
Average velocity:
¾
= displacement divided by time interval
±
A vector pointing from initial to final position
¾
Vector notation:
¾
2D:
t
∆
∆
=
r
v
k
j
i
r
v
⋅
+
⋅
+
⋅
≡
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
≡
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
∆
∆
∆
∆
∆
∆
≡
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
∆
∆
∆
∆
≡
∆
∆
≡
z
y
x
z
y
x
v
v
v
v
v
v
t
z
t
y
t
x
z
y
x
t
t
1
j
i
v
⋅
+
⋅
≡
y
x
v
v

Physics 1301: Chapter 2, Pg 5
Distance traveled and average speed
Distance traveled (path of motion)
¾
= a positive scalar equal to the length of a part of the
trajectory between initial and final points
Average speed:
¾
= distance traveled divided by time interval
±
Speed is a positive scalar
t
l
s
∆
∆
≡
r
∆
≥
∆
l
v
≥
s
∫
≡
∆
Path
dl
l

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*Sign up*Physics 1301: Chapter 2, Pg 6
Velocity and speed
Velocity:
¾
= time derivative of position
±
A vector pointing in the
direction of motion
±
A tangent to the trajectory
Speed:
¾
= time derivative of the
distance traveled
¾
= magnitude of velocity
dt
d
r
v
≡
v
dt
d
dt
d
dt
dl
s
≡
≡
≡
≡
≡
v
r
r