Translational Motion
Projectile Motion
Circular Motion
Motion Map
•  Which direction is the object moving?
Tactics: Vector Addition
Working in groups of 3, do two examples of vector addition
-on your whiteboard, draw two random vectors, then add
them graphically
Tactics: Vector Subtraction
Working in groups of 3, do two examples of vector subraction
-on your whiteboard, draw two random vectors, then add
them graphically
The Displacement vector
Using vector subtraction and working on the whiteboards,
show how you get this vector, Δr
1
r0
Δr
2
r1
Average Speed, Average Velocity
To quantify an object’s fastness or slowness, we define
a ratio as follows:
Average speed does not include information about
direction of motion. Average velocity does include
direction. The average velocity of an object during a time
interval Δt, in which the object undergoes a displacement
Δr, is the vector
Motion Map
•  Displacement vectors
•  Velocity Vectors
Δr4
v4Δt
Δr3
v3Δt
Δr2 Δr1 Δr0
v2Δt
v1Δt v0Δt
Motion Map
•  Δt is the same between each position,
so we can drop it
•  Velocity, v, is proportional to
displacement, Δr
v4
v3
v2
v1
v0
Motion Diagrams with Velocity Vectors
Linear Acceleration
Because velocity is a vector, it can change in two
possible ways.
1.  The magnitude can change, indicating a change in
speed, or
2.  The direction can change, indicating that the object
has changed direction.
We will concentrate for now on the first case, a change
in speed.
aavg
Δv
≡
= slope of the velocity - versus - time graph
Δt
Tactics: Finding the acceleration vector
Tactics: Finding the acceleration vector

Δv = a⋅ Δt
€
Complete a motion diagram and find the acceleration for
an object moving:
Down an incline while speeding up
Up an incline while slowing down
A particle undergoes acceleration while
moving from point 1 to point 2. Which of
the choices shows the velocity vector as
the object moves away from point 2?
A particle undergoes acceleration while
moving from point 1 to point 2. Which of
the choices shows the velocity vector as
the object moves away from point 2?
EXAMPLE 1.7 Interpreting a position graph
EXAMPLE 1.7 Interpreting a position graph
Tactics: Drawing a pictorial representation
Tactics: Drawing a pictorial representation
General Problem-Solving Strategy
Draw a Pictorial Representation
•  Jane slams on her brakes while driving 30
mph and skids to a halt in 60 feet. How long
does it take her to come to a stop?
•  Analyze the graph.
Describe the motion
by creating a
pictorial
representation.
Position (m)
Graphical Representation
6
4
2
2
6
8
Time (s)
Upcoming Assignments
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before class on Tuesday
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before class on Thursday
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