warm up. constant velocity constant velocity = no change in velocity definition of acceleration =...
TRANSCRIPT
Warm Up
Constant Velocity
CONSTANT VELOCITY = NO CHANGE IN VELOCITY
Definition of acceleration = CHANGE IN VELOCITY over a period of time
CONSTANT VELOCITY = 0 ACCLERATION
Position/Time and Velocity/Time
The graph to the right shows the velocity graph for the position graph to the left.
Position vs. Time Graphs
Curved line = changing velocity
Accelerated motion
Velocity vs. Time Graphs
Straight line = velocity changing at a constant rate
Constant acceleration
Velocity vs. Time Graphs
What is in a velocity vs. time graph? X-axis: time (s) that the object is in
motion Y-axis: velocity (m/s) of the object in
motionSLOPE =
ACCELERATION of the
object
Velocity vs. Time Graphs
Slope = rise = Δv run Δt = How much your VELOCITY is
changing
How much your time is changing
= ∆v = acceleration!
∆t
SLOPE OF V vs T graph EQUALS ACCELERATION!!!
Between which letters is velocity increasing? Between which letters is velocity decreasing? Between which letters is velocity constant? Is there anywhere that the object is not
moving? Does the object change direction?
When velocity increases, the acceleration is:
When the velocity decreases, the acceleration is:
When the velocity remains constant, the acceleration is:
MOTION DIAGRAM
Position vs. Time VERSUS Velocity vs. Time
Position vs. Time Graph
Velocity vs. Time Graph
X-axis
Y-axis
Slope
Steeper line means…
Horizontal line means…
Downward sloping line means…
Time (s) Time (s)
Position (m) Velocity (m/s)
Velocity (m/s) Acceleration (m/s2)Faster velocity Speeding up
No velocity = at rest
Constant velocity = no acceleration
Moving backwards/Negative velocity
Slowing down
Create the matching velocity vs. time graph:
Answer on next click
0 5 10 15 20 25 30
-1.5
-1
-0.5
0
0.5
1
1.5
2
velocity vs time (answer)
Time (s)
Velo
city
(m
/s)
Displacement from V vs T
To find the displacement, calculate the area under the curve of a velocity-time graph!
Example
Consider the position vs time graph on the back of your homework…
Example 1
1. What does the slope of the graph measure? (if anything)
2. What does the area of the graph measure? (if anything)
3. Describe the motion of the object 4. What is the position of the object at 2 seconds?5. What is the velocity of the object from 2 - 3
seconds?6. What is the acceleration between 2-3 seconds?
Example 1
1. What does the slope of the graph measure? (if anything) - Slope measures the velocity.2. What does the area of the graph measure? (if anything)- Area has no meaning.3. Describe the motion of the object - The object is moving at a constant positive velocity from 2m before stopping at 5 for a second. The object then returns with a negative velocity to its starting position and continues past the starting position to 1 m. What is the position of the object at 2 seconds?
Example 1
4. What is the position of the object at 2 seconds?- 4 m5. What is the velocity of the object from 2 - 3 seconds?- 1 m/s6. What is the acceleration between 2-3 seconds?- 0 m/s2 because the velocity is constant.
Example 2
1. What does the slope of the graph measure? (if anything)2. What does the area of the graph measure? (if anything)3. Describe the motion of the object4. What is the velocity of the object at 2 seconds?5. What is the acceleration of the object from 2-3 seconds?6. What is the change of position between 2 and 3
seconds?
Example 2
1. What does the slope of the graph measure? (if anything)- The acceleration2. What does the area of the graph measure? (if anything)- The position3. Describe the motion of the object- The object is accelerating away from its initial position in the positive direction before maintaining a constant velocity for 1 second. The object then continues moving in the positive direction as it decelerates to 1 m/s.
Example 2
4. What is the velocity of the object at 2 seconds?- 4 m/s5. What is the acceleration of the object from 2-3 seconds?1 m/s2
6. What is the change of position between 2 and 3 seconds?- 4.5 m (Area of a trapezoid with base 4 and base 5 and height 1)
Exit Question
Draw a velocity – time graph of someone walking away from a motion detector at 2 m/s, then standing still, then walking toward at 1 m/s.