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 motion SLOPE = 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 GraphVelocity vs. Time Graph X-axis Y-axis Slope Steeper line means… Horizontal line means… Downward sloping line means… Time (s) Position (m)Velocity (m/s) Acceleration (m/s 2 ) 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

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 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 m 5. What is the velocity of the object from seconds? - 1 m/s 6. What is the acceleration between 2-3 seconds? - 0 m/s 2 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 object 4. 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 acceleration 2. What does the area of the graph measure? (if anything) - The position 3. 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/s 5. What is the acceleration of the object from 2-3 seconds? 1 m/s 2 6. What is the change of position between 2 and 3 seconds? 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.