Position-Time and Velocity-Time Graphs in Physics
Explore the characteristics of position-time graphs, including constant speed, rest, acceleration, deceleration, and velocity translation. Understand how features on one graph correlate to features on another for effective analysis in physics.
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Presentation Transcript
Sections 2.2-2.3 Position-Time and Velocity-Time Graphs
Questions for Consideration What is a position-time graph from Unit 1? What is a velocity-time graph? How do features on one graph translate into features on the other?
Position-Time Graphs Show an object s position as a function of time. x-axis: time y-axis: position
Position-Time Graphs What are the characteristics of this graph? Straight line, upward slope What kind of motion created this graph? Constant speed 10 9 8 7 6 position (cm) 5 4 3 2 1 time (s) 1 2 3 4 5 6 7 9 10 8
Position-Time Graphs Each type of motion has a characteristic shape on a P-T graph. Constant speed Zero speed (at rest) Accelerating (speeding up) Decelerating (slowing down)
Position-Time Graphs Constant speed is represented by a sloped, straight segment on the P-T graph. pos. (m) pos. (m) time (s) time (s) Constant speed in positive direction. Constant speed in negative direction.
Position-Time Graphs A horizontal segment means the object is at rest. pos. (m) time (s)
Position-Time Graphs Curved segments that get steeper on the P-T graph mean the object s speeding up pos. (m) pos. (m) time (s) time (s) Speeding up in positive direction. Speeding up in negative direction.
Position-Time Graphs Curved segments that level off on the P- T graph mean the object s slowing down pos. (m) pos. (m) time (s) time (s) Traveling in positive direction but slowing down. Traveling in negative direction but slowing down.
Position-Time Graphs The slope of a P-T graph is equal to the object s velocity in that segment. change in y change in x slope = 50 position (m) 40 (30 m 10 m) (30 s 0 s) 30 slope = 20 (20 m) (30 s) 10 slope = 10 20 30 40 time (s) slope = 0.67 m/s
Position-Time Graphs The following P-T graph corresponds to an object moving back and forth along a straight path. Can you describe its movement based on the graph? N position (m) time (s) S
Velocity-Time Graphs A velocity-time (V-T) graph shows an object s velocity as a function of time. A horizontal line = constant velocity. A straight sloped line = constant acceleration. Acceleration = change in velocity over time. Positive slope = positive acceleration. Not necessarily speeding up! Negative slope = negative acceleration. Not necessarily slowing down!
Velocity-Time Graphs A horizontal line on the V-T graph means constant velocity. + Object is moving at a constant velocity in the + direction velocity (m/s) time (s) -
Velocity-Time Graphs A horizontal line on the V-T graph means constant velocity. + Object is moving at a constant velocity in - direction velocity (m/s) time (s) -
Velocity-Time Graphs If an object isn t moving, its velocity is zero. + Object is at rest velocity (m/s) time (s) -
Velocity-Time Graphs If the V-T line has a positive slope, the object is undergoing acceleration in positive direction. If v is in positive quadrant, object is speeding up. If v is in negative quadrant, object is slowing down.
Velocity-Time Graphs V-T graph has positive slope. + + velocity (m/s) velocity (m/s) time (s) time (s) Negative velocity and positive slope,: object is slowing down. Positive velocity and positive slope: object is speeding up! - -
Velocity-Time Graphs If the V-T line has a negative slope, the object is undergoing acceleration in the negative direction. If v is positive, the object is slowing down. If v is negative also, the object is speeding up.
Velocity-Time Graphs V-T graph has negative slope. + + velocity (m/s) velocity (m/s) time (s) time (s) Negative velocity and negative acceleration: object is speeding up! (in negative direction) Positive velocity and negative acceleration: object is slowing down, - -
Assignment Worksheets on P-T and V-T graphs
