Position-Time and Velocity-Time Graphs Questions for Consideration What is a position-time graph? 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 Imagine a ball rolling along a table, illuminated by a strobe light every second. 0s 1s 2s 3s 4s 5s 6s 7s 8s You can plot the ball’s position as a function of time. 9 s 10 s Position-Time Graphs 10 9 position (cm) 8 7 6 5 4 3 2 1 time (s) 1 2 3 4 5 6 7 8 9 10 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 position (cm) 6 5 4 3 2 1 time (s) 1 2 3 4 5 6 7 8 9 10 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 straight segment on the P-T graph. time (s) Constant speed in positive direction. pos. (m) pos. (m) time (s) Constant speed in negative direction. Position-Time Graphs Constant speed is represented by a straight segment on the P-T graph. pos. (m) time (s) A horizontal segment means the object is at rest. Position-Time Graphs time (s) Speeding up in positive direction. pos. (m) Curved segments on the P-T graph mean the object’s speed is changing. pos. (m) time (s) Speeding up in negative direction. Position-Time Graphs time (s) Traveling in positive direction, but slowing down. pos. (m) Curved segments on the P-T graph mean the object’s speed is changing. pos. (m) time (s) 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 slope = 50 position (m) 40 change in x (30 m – 10 m) 30 slope = (30 s – 0 s) 20 (20 m) 10 slope = 10 20 time (s) 30 (30 s) 40 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) S time (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. Positive slope = positive acceleration. Acceleration = change in velocity over time. 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. velocity (m/s) N S time (s) Object is moving at a constant velocity North. Velocity-Time Graphs A horizontal line on the V-T graph means constant velocity. velocity (m/s) N S time (s) Object is moving at a constant velocity South. Velocity-Time Graphs If an object isn’t moving, its velocity is zero. N velocity (m/s) S Object is at rest 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 positive also, object is speeding up. If v is negative, object is slowing down. Velocity-Time Graphs V-T graph has positive slope. N velocity (m/s) N S time (s) Positive velocity and positive acceleration: object is speeding up! velocity (m/s) S time (s) Negative velocity and positive acceleration: object is slowing down. 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. N velocity (m/s) N S time (s) Positive velocity and negative acceleration: object is slowing down, velocity (m/s) S time (s) Negative velocity and negative acceleration: object is speeding up! (in negative direction)