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**Position-Time and Velocity-Time Graphs**

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**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?

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**Position-Time Graphs Show an object’s position as a function of time.**

x-axis: time y-axis: position Slope = average velocity

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**Position-Time Graphs 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 s 8 s 9 s 10 s**

Imagine a ball rolling along a table, illuminated by a strobe light every second. You can plot the ball’s position as a function of time. 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 s 8 s 9 s 10 s

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Position-Time Graphs 1 2 3 4 5 6 7 8 9 10 position (cm) time (s)

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**Position-Time Graphs What are the characteristics of this graph?**

Straight line, upward slope What kind of motion created this graph? Constant velocity 1 2 3 4 5 6 7 8 9 10 time (s) position (cm)

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Position-Time Graphs Each type of motion has a characteristic shape on a P-T graph. Zero speed (at rest) Constant velocity Accelerating

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Position-Time Graphs Constant velocity is represented by a straight segment on the P-T graph. time (s) pos. (m) Constant velocity in positive direction. time (s) pos. (m) Constant velocity in negative direction.

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Position-Time Graphs An object not moving is represented by a straight segment on the P-T graph. time (s) pos. (m) A horizontal segment means the object is at rest.

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Position-Time Graphs Curved segments on the P-T graph mean the object’s velocity is changing. time (s) pos. (m) Increasing velocity in positive direction. time (s) pos. (m) Increasing velocity in negative direction.

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Position-Time Graphs The slope of a P-T graph is equal to the object’s velocity in that segment. slope = change in y change in x time (s) position (m) 10 20 30 40 50 slope = (30 m – 10 m) (30 s – 0 s) slope = (20 m) (30 s) slope = 0.67 m/s

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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? time (s) position (m) N S

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**5.2 Velocity vs. Time X-axis is the “time” Y-axis is the “velocity”**

Slope of the line = average acceleration

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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. Negative slope = negative acceleration. Not necessarily slowing down!

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Velocity-Time Graphs A horizontal line on the V-T graph means constant velocity so no acceleration. time (s) velocity (m/s) N S Object is moving at a constant velocity North.

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Velocity-Time Graphs A horizontal line on the V-T graph means constant velocity. time (s) velocity (m/s) N S Object is moving at a constant velocity South.

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**Velocity-Time Graphs If an object isn’t moving, its velocity is zero.**

time (s) velocity (m/s) N S Object is at rest

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**Velocity vs. Time Horizontal lines = constant velocity**

Sloped line = changing velocity Steeper = greater change in velocity per second

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Velocity-Time Graphs If the V-T line has a positive slope, the object is undergoing acceleration in positive direction.

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**Velocity-Time Graphs V-T graph has positive slope. N S**

time (s) velocity (m/s) N S Positive velocity and constant positive acceleration

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**Slope of V vs. T graph Slope = rise/run**

Pick two points on the line: (0,0) (2,2) Slope = (2-0)/(2-0) = 1.0 m/s2 Slope = Average acceleration of the object

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Velocity-Time Graphs If the V-T line has a negative slope, the object is undergoing acceleration in the negative direction.

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**Velocity-Time Graphs V-T graph has negative slope. N S**

time (s) velocity (m/s) N S Positive velocity and negative acceleration: object is slowing down, time (s) velocity (m/s) N S Negative velocity and negative acceleration: object is speeding up! (in negative direction)

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