2 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?
3 Position-Time Graphs Show an object’s position as a function of time. x-axis: timey-axis: positionSlope = average velocity
4 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 s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s
5 Position-Time Graphs12345678910position (cm)time (s)
6 Position-Time Graphs What are the characteristics of this graph? Straight line, upward slopeWhat kind of motion created this graph?Constant velocity12345678910time (s)position (cm)
7 Position-Time GraphsEach type of motion has a characteristic shape on a P-T graph.Zero speed (at rest)Constant velocityAccelerating
8 Position-Time GraphsConstant 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.
9 Position-Time GraphsAn 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.
10 Position-Time GraphsCurved 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.
11 Position-Time GraphsThe slope of a P-T graph is equal to the object’s velocity in that segment.slope =change in ychange in xtime (s)position (m)1020304050slope =(30 m – 10 m)(30 s – 0 s)slope =(20 m)(30 s)slope = 0.67 m/s
12 Position-Time GraphsThe 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)NS
13 5.2 Velocity vs. Time X-axis is the “time” Y-axis is the “velocity” Slope of the line = average acceleration
14 Velocity-Time GraphsA 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!
15 Velocity-Time GraphsA horizontal line on the V-T graph means constant velocity so no acceleration.time (s)velocity (m/s)NSObject is moving at a constant velocity North.
16 Velocity-Time GraphsA horizontal line on the V-T graph means constant velocity.time (s)velocity (m/s)NSObject is moving at a constant velocity South.
17 Velocity-Time Graphs If an object isn’t moving, its velocity is zero. time (s)velocity (m/s)NSObject is at rest
18 Velocity vs. Time Horizontal lines = constant velocity Sloped line = changing velocitySteeper = greater change in velocity per second
19 Velocity-Time GraphsIf the V-T line has a positive slope, the object is undergoing acceleration in positive direction.
20 Velocity-Time Graphs V-T graph has positive slope. N S time (s)velocity (m/s)NSPositive velocity and constant positive acceleration
21 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/s2Slope = Average acceleration of the object
22 Velocity-Time GraphsIf the V-T line has a negative slope, the object is undergoing acceleration in the negative direction.
23 Velocity-Time Graphs V-T graph has negative slope. N S time (s)velocity (m/s)NSPositive velocity and negative acceleration: object is slowing down,time (s)velocity (m/s)NSNegative velocity and negative acceleration: object is speeding up! (in negative direction)