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Kinematics:What is velocity and
acceleration?
Let’s Review
v = d t
Distance traveled (m)
Time taken (sec)
Average Velocity (m/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
0
av
tt
x
t
x
Motion Graphs
0
x av
ttt
x
Starting Point Direction Velocity Acceleration
0 + Positive + V (speeding up) +constant
Acceleration Example #1
Δv from +5 to +10 m/s requiresa +5 m/s/s acceleration!
V (m/s) a (m/s/s)
0 +5
+ 5 + 5
+10 + 5
15 + 5
Motion Graphs
0
av
ttt
x
x
Starting Point Direction Velocity Acceleration
Positive (+) +V (slowing down) -constant
0
Acceleration Example #2
V (m/s) a (m/s/s)
+ 10 - 5
+ 5 - 5
0 - 5
Δv from +10 to + 5 m/s requiresa - 5 m/s/s acceleration!
Motion Graphs
0
x a
tt
v
t
x
Starting Point Direction Velocity Acceleration
above negative (-)
-V (speeding up) -constant
Acceleration Example #3
Δv from -5 to -10 m/s requiresa -5 m/s/s acceleration!
Direction is negative (-), velocity is increasing (+)Therefore acceleration is (-)
V (m/s) a (m/s/s)
0 -5
- 5 - 5
-10 - 5
-15 - 5
Motion Graphs
0
a
t
x
t
x
v
t
Starting Point Direction Velocity Acceleration
above negative (-) - V (slowing down)
+constant
Acceleration Example #4
V (m/s) a (m/s/s)
- 10 + 5
- 5 + 5
0 + 5
Δv from -10 to -5 m/s requiresa +5 m/s/s acceleration!
Direction is (-), velocity is slowing down (-)Therefore acceleration is (+)
Summary of Velocity & Acceleration
V E L O C I T Y ACCELERATION
+ -
+Moving positive
direction; Speeding up
+ acceleration
Moving negative
direction; Slowing down
- acceleration
-
Moving positive
direction; Slowing down
- acceleration
Moving negative
direction; Speeding up
+ acceleration
Direction of Motion Action/Sign of Velocity
Sign of Acceleration
Determining signs for velocity and acceleration
Increasing speed
+ direction+
Decreasing
speed + direction
-
-
Increasing speed
- direction
Decreasing speed
- direction
+