Kinematics:
What is velocity and acceleration?
Let’s Review
Average Velocity
(m/sec)
v=d
t
Distance traveled (m)
Time taken (sec)
Instantaneous Velocity: the speed at any given
moment (like what your speedometer shows)
Slope of Position vs Time graph is the Average
Velocity
 The slope of a line is the ratio of the “rise” (vertical
change) to the “run”(horizontal change) of the line.
Constant Speed
 On a Velocity vs Time graph constant velocity is a
straight line
Area under the velocity vs time graph is equal to the
distance travelled.
What is a Motion Diagram?
 Motion Diagram: Is a more sophisticated dot
diagram that conveys more information about the
situation.
•What do the arrows indicate?
•What does the length of each arrow indicate about the
motion of the object?
Change in Velocity
 What must you do to the first velocity arrow to get
the second velocity arrow? What direction? How
much?
•The arrow you drew to show the difference between the
velocity arrows is called a ∆v or change in velocity arrow.
•What does the ∆v arrow tell you about the motion of the
object?
Let’s Try!
Lesson 11: Speeding Index
Motion of a Falling Object
 Using the video of the falling object we have collected the
following data:
 Draw a motion diagram.
 Plot a position time graph.
 Does this object represent an object with constant velocity?
Explain how you know.
What is Acceleration?
 Acceleration is a vector quantity that is defined as the rate
at which an object changes its velocity
 There are 3 types of acceleration:



If an object is increasing in speed (+ acceleration)
If an object is decreasing in speed (- acceleration, also called
deceleration)
Or if the object changes direction (+ or -)
How do we calculate Acceleration?
 Acceleration is the change in speed over the change in time.
 The slope of the speed versus time graph is the acceleration.
How to Solve Motion Problems
Rearrange the equation to get final velocity
How do we determine the distance travelled by the object if
velocity is changing?
Equations to Remember
Motion Graphs
x
v
t
x
0
a
t
t
Motion Graphs
x
v
t
a
t
t
x
0
Starting Point
0
Direction
+ Positive
Velocity
+ V (speeding up)
Acceleration
+constant
Acceleration Example #1
V (m/s) a (m/s/s)
0
+5
+5
+5
+10
+5
15
+5
Δv from +5 to +10 m/s requires
a +5 m/s/s acceleration!
Motion Graphs
x
v
t
a
t
t
x
0
Starting Point
Direction
0
Positive (+)
Velocity
+V (slowing down)
Acceleration
-constant
Acceleration Example #2
V (m/s) a (m/s/s)
+ 10
-5
+ 5
-5
0
-5
Δv from +10 to + 5 m/s requires
a - 5 m/s/s acceleration!
Motion Graphs
x
v
t
a
t
t
x
0
Starting Point
above
Direction
negative (-)
Velocity
-V (speeding up)
Acceleration
-constant
Acceleration Example #3
V (m/s)
a (m/s/s)
0
-5
-5
-5
-10
-5
-15
-5
Δv from -5 to -10 m/s requires
a -5 m/s/s acceleration!
Direction is negative (-), velocity is increasing (+)
Therefore acceleration is (-)
Motion Graphs
a
v
x
t
t
t
x
0
Starting Point
above
Direction
negative (-)
Velocity
- V (slowing down)
Acceleration
+constant
Acceleration Example #4
V (m/s) a (m/s/s)
- 10
+5
- 5
+5
0
+5
Δv from -10 to -5 m/s requires
a +5 m/s/s acceleration!
Direction is (-), velocity is slowing down (-)
Therefore acceleration is (+)
Summary of Velocity & Acceleration
VELOCITY
A
C
C
E
L
E
R
A
T
I
O
N
+
-
+
-
Moving positive
Moving negative
direction; Speeding up
direction; Slowing down
+ acceleration
- acceleration
Moving positive
Moving negative
direction; Slowing down
direction; Speeding up
- acceleration
+ acceleration
Determining signs for velocity and acceleration
Direction of Motion
Action/Sign of
Velocity
Sign of
Acceleration
Increasing speed
+ direction
Decreasing speed
+ direction
Increasing speed
- direction
Decreasing speed
- direction
+
+