P-T Slope

7/2/2015 Position-Time Graphs 2 Constant Velocity Constant Velocity Consider a car moving with a constant, rightward (+) velocity - say of +10 m/s.Consider a car moving with a constant, rightward (+) velocity - say of +10 m/s.

7/2/2015 Position-Time Graphs 3 Graph of Constant Velocity If the position-time data for such a car were graphed, then the resulting graph would look like the graph at the right.If the position-time data for such a car were graphed, then the resulting graph would look like the graph at the right.

7/2/2015 Position-Time Graphs 4 Motion described as a constant, positive velocity results in a line of constant and positive slope when plotted as a position- time graph.Motion described as a constant, positive velocity results in a line of constant and positive slope when plotted as a position- time graph. Constant Velocity

7/2/2015 Position-Time Graphs 5 The Meaning of Slope of p-t Graphs The slope of a position vs. time graph reveals pertinent information about an object's velocity. For example:The slope of a position vs. time graph reveals pertinent information about an object's velocity. For example: –a small slope = small velocity –a negative slope = negative velocity –a constant slope (straight line) = constant velocity –a changing slope (curved line) = changing velocity (more on this later).

7/2/2015 Position-Time Graphs 6 Slope of a p-t Graph The actual slope value of any straight line on a graph is the velocity of the object.The actual slope value of any straight line on a graph is the velocity of the object. Slope = VelocitySlope = Velocity

7/2/2015 Position-Time Graphs 7 Example 1 Consider a car moving with a constant velocity of +10 m/s for 5 seconds. The diagram below depicts such a motion.Consider a car moving with a constant velocity of +10 m/s for 5 seconds. The diagram below depicts such a motion.

7/2/2015 Position-Time Graphs 8 Graph-Example 1 The position-time graph would look like the graph at the right.The position-time graph would look like the graph at the right. Note that during the first 5 seconds, the line on the graph slopes up 10 m for every 1 second along the horizontal (time) axis.Note that during the first 5 seconds, the line on the graph slopes up 10 m for every 1 second along the horizontal (time) axis.

7/2/2015 Position-Time Graphs 9 Calculating Slope  Pick two points on the line and determine their coordinates.  Determine the difference in y-coordinates of these two points (rise).  Determine the difference in x-coordinates for these two points (run).  Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

7/2/2015 Position-Time Graphs 10 Calculate the slopeCalculate the slope y 2 – y 1 = d f – d i = rise x 2 – x 1 t f – t i run 50-0m = 50m = 10 m 5-0 s 5s s 5-0 s 5s s Graph-Example 1

7/2/2015 Position-Time Graphs 11 Example 2 Now consider a car moving at a constant velocity of +5 m/s for 5 seconds, abruptly stopping, and then remaining at rest (v = 0 m/s) for 5 seconds.Now consider a car moving at a constant velocity of +5 m/s for 5 seconds, abruptly stopping, and then remaining at rest (v = 0 m/s) for 5 seconds.

7/2/2015 Position-Time Graphs 12 Graph-Example 2 slope = d f – d i t f – t i 25-0m = 25m = +5 m 5-0 s 5s s slope = d f – d i t f – t i 25-25m = 0m = 0 m 10-5 s 5s s

7/2/2015 Position-Time Graphs 13 Note A slope of zero means that the object is at rest (not moving).A slope of zero means that the object is at rest (not moving).

7/2/2015 Position-Time Graphs 14 Slope Principle The principle is: the slope of the line on a position-time graph is equal to the velocity of the object.The principle is: the slope of the line on a position-time graph is equal to the velocity of the object. If the object is moving with a velocity of +4 m/s, then the slope of the line will be +4 m/s.If the object is moving with a velocity of +4 m/s, then the slope of the line will be +4 m/s.

7/2/2015 Position-Time Graphs 15 3 Trials

7/2/2015 Position-Time Graphs 16 Interpretation of p-t Graphs Recall:Recall: –On a p-t graph a negative slope means that the object is moving in the negative direction. –A positive slope means that the object is moving in the positive direction. –No slope (zero) means that the object is at rest.

7/2/2015 Position-Time Graphs 17 Interpretation of p-t Graphs Calculate slope for the following timeframes: 0s – 10s 10s – 15s 15s – 40s 40s – 55s