Activity 4: Working with Velocity Graphs
Focus for this activity
Once again in this activity we are going to be working with a very simple model of a train system. 

As before, in the model, the train starts out at Station A, goes to Station B to pick up a passenger, and then returns to Station A. Station A will be 1.5 meters in front of a motion probe, and Station B will be 0.5 meters in front of the motion probe.

In this activity, we will be looking at velocity, rather than position.

Velocity is similar to speed, except that it can be positive or negative. For example, it may be positive if you are going toward something, and then negative when you are going away. You can think of it as "speed in the opposite direction" when the sign of a velocity is negative.


How familiar are you with negative numbers? 1. I'm not familiar with negative numbers. 2. I have worked with them a little. 3. I am familiar enough with them to add and subtract them. 4. I am familiar enough to multiply them.
Prediction
As before, you will be making graphs while moving from Station A to Station B, and then back to Station A.
Can you predict what a velocity graph might look like? Using the pencil tool, (to the right) draw what you think the graph will look like.
When you have finished, please submit your graph by clicking the SUBMIT button below the graph.




-0.013850415 -0.0 0.0 -0.0 0.013850415 -0.009259259 0.02770083 -0.009259259 0.041551247 -0.0 0.05540166 0.009259259 0.06925208 0.009259259 0.083102494 0.009259259 0.09695291 0.009259259 0.11080332 0.009259259 0.12465374 0.009259259 0.13850416 0.009259259 0.15235457 0.018518519 0.16620499 0.027777778 0.1800554 0.046296295 0.19390582 0.046296295 0.20775624 0.046296295 0.23545706 0.055555556 0.24930748 0.06481481 0.2631579 0.06481481 0.27700832 0.074074075 0.29085872 0.074074075 0.30470914 0.074074075 0.31855956 0.074074075 0.33240998 0.074074075 0.3462604 0.074074075 0.3601108 0.074074075 0.3739612 0.083333336 0.38781163 0.083333336 0.40166205 0.083333336 0.41551247 0.083333336 0.4293629 0.083333336 0.44321328 0.083333336 0.4570637 0.09259259 0.47091413 0.09259259 0.48476455 0.09259259 0.49861497 0.09259259 0.51246536 0.10185185 0.5263158 0.10185185 0.5401662 0.11111111 0.55401665 0.11111111 0.56786704 0.11111111 0.58171743 0.11111111 0.5955679 0.12037037 0.6094183 0.12037037 0.6371191 0.12962963 0.6509695 0.1388889 0.66481996 0.14814815 0.67867035 0.14814815 0.6925208 0.1574074 0.7063712 0.1574074 0.7202216 0.17592593 0.734072 0.17592593 0.7479224 0.17592593 0.7617729 0.17592593 0.77562326 0.18518518 0.7894737 0.18518518 0.8033241 0.18518518 0.8171745 0.18518518 0.83102494 0.19444445 0.84487534 0.19444445 0.8587258 0.19444445 0.8725762 0.19444445 0.900277 0.2037037 0.9141274 0.2037037 0.92797786 0.2037037 0.94182825 0.2037037 0.95567864 0.2037037 0.9695291 0.2037037 0.99722993 0.2037037 1.0110804 0.2037037 1.0387812 0.2037037 1.0526316 0.2037037 1.1080333 0.2037037 1.1357341 0.2037037 1.1495845 0.2037037 1.2049861 0.2037037 1.2188365 0.2037037 1.232687 0.2037037 1.2465374 0.2037037 1.2603878 0.2037037 1.2742382 0.2037037 1.2880887 0.21296297 1.301939 0.22222222 1.3157895 0.22222222 1.3434904 0.23148148 1.3711911 0.24074075 1.3850416 0.24074075 1.4127424 0.24074075 1.4265928 0.24074075 1.4404432 0.24074075 1.4542936 0.25 1.4958448 0.25925925 1.5235457 0.25925925 1.5512465 0.2685185 1.565097 0.2685185 1.5789474 0.2685185 1.5927978 0.2685185 1.6066482 0.2685185 1.6204987 0.2685185 1.634349 0.2685185 1.6481994 0.2685185 1.6620499 0.2685185 1.6759002 0.2685185 1.6897507 0.2685185 1.7036011 0.2685185 1.7174516 0.2685185 1.7313019 0.2685185 1.7590028 0.2685185 1.7728531 0.2685185 1.7867036 0.2685185 1.8144045 0.2685185 1.8559557 0.2685185 1.8836565 0.25925925 1.9252077 0.25 1.9806094 0.25 2.0083103 0.24074075 2.0221608 0.24074075 2.0498614 0.23148148 2.063712 0.23148148 2.0775623 0.23148148 2.1052632 0.23148148 2.1191137 0.23148148 2.1468143 0.23148148 2.1745152 0.22222222 2.1883657 0.22222222 2.2022161 0.22222222 2.2160666 0.22222222 2.2299168 0.22222222 2.2437673 0.22222222 2.2576177 0.21296297 2.2853186 0.19444445 2.3130193 0.19444445 2.396122 0.16666667 2.4515235 0.14814815 2.465374 0.14814815 2.4792244 0.1388889 2.493075 0.1388889 2.506925 0.1388889 2.5207756 0.1388889 2.534626 0.12962963 2.5484765 0.12962963 2.562327 0.12962963 2.5761774 0.12037037 2.603878 0.11111111 2.6177285 0.10185185 2.6592798 0.083333336 2.6731303 0.083333336 2.6869807 0.083333336 2.700831 0.074074075 2.7146814 0.06481481 2.7285318 0.06481481 2.7423823 0.06481481 2.7562327 0.055555556 2.7700832 0.046296295 2.7839334 0.037037037 2.7977839 0.027777778 2.8116343 0.018518519 2.8254848 0.009259259 2.8393352 -0.0 2.8531857 -0.009259259 2.867036 -0.018518519 2.8808863 -0.018518519 2.8947368 -0.027777778 2.9085872 -0.037037037 2.9224377 -0.046296295 2.9501386 -0.046296295 2.963989 -0.046296295 3.0055401 -0.055555556 3.0193906 -0.055555556 3.0470915 -0.06481481 3.060942 -0.06481481 3.0747921 -0.06481481 3.0886426 -0.06481481 3.102493 -0.06481481 3.130194 -0.06481481 3.1440444 -0.074074075 3.1578948 -0.074074075 3.171745 -0.074074075 3.1855955 -0.074074075 3.2132964 -0.074074075 3.2409973 -0.074074075 3.2825484 -0.074074075 3.2963989 -0.09259259 3.3102493 -0.10185185 3.3240998 -0.10185185 3.3379502 -0.10185185 3.3795013 -0.12037037 3.4072022 -0.12037037 3.4349031 -0.12962963 3.4487534 -0.1388889 3.4626038 -0.1388889 3.4764543 -0.14814815 3.5734072 -0.16666667 3.6149585 -0.17592593 3.6426592 -0.17592593 3.698061 -0.19444445 3.739612 -0.19444445 3.767313 -0.19444445 3.795014 -0.2037037 3.8088644 -0.2037037 3.8504155 -0.2037037 3.864266 -0.2037037 3.8919668 -0.2037037 3.9058173 -0.2037037 3.933518 -0.2037037 3.9750693 -0.2037037 3.9889197 -0.2037037 4.030471 -0.2037037 4.0581717 -0.2037037 4.072022 -0.2037037 4.1135736 -0.2037037 4.1412745 -0.2037037 4.168975 -0.2037037 4.1828256 -0.2037037 4.196676 -0.2037037 4.2105265 -0.2037037 4.2243767 -0.2037037 4.2520776 -0.2037037 4.265928 -0.2037037 4.2797785 -0.2037037 4.2936287 -0.2037037 4.3213296 -0.2037037 4.3351803 -0.2037037 4.3628807 -0.2037037 4.3905816 -0.2037037 4.432133 -0.2037037 4.4459834 -0.2037037 4.4736843 -0.2037037 4.5152354 -0.2037037 4.5290856 -0.2037037 4.5567865 -0.2037037 4.5844874 -0.2037037 4.598338 -0.18518518 4.6260386 -0.18518518 4.66759 -0.16666667 4.7229915 -0.1574074 4.764543 -0.14814815 4.792244 -0.1388889 4.8199444 -0.12962963 4.8476453 -0.12037037 4.861496 -0.11111111 4.875346 -0.10185185 4.903047 -0.083333336 4.958449 -0.06481481 4.972299 -0.055555556 4.98615 -0.046296295 5.0 -0.037037037 5.027701 -0.018518519 5.055402 -0.0 5.33241 0.12037037 5.4570637 0.19444445 5.498615 0.21296297 5.6371193 0.24074075 5.6925206 0.25 5.7756233 0.25 5.7894735 0.25 5.8171744 0.25 5.831025 0.25 5.8448753 0.25 5.8587255 0.25 5.872576 0.25 5.8864264 0.25 5.900277 0.25 5.927978 0.25 5.9556785 0.25 5.9833794 0.25 6.038781 0.25 6.066482 0.25 6.191136 0.24074075 6.260388 0.24074075 6.32964 0.24074075 6.3850417 0.24074075 6.440443 0.23148148 6.4819946 0.23148148 6.495845 0.23148148 6.5235457 0.23148148 6.537396 0.23148148 6.5512466 0.23148148 6.5789475 0.23148148 6.5927978 0.23148148 6.6204987 0.23148148 6.634349 0.23148148 6.703601 0.23148148 6.7174516 0.23148148 6.7590027 0.23148148 6.8282547 0.21296297 6.8975067 0.19444445 6.9113574 0.18518518 6.966759 0.17592593 7.036011 0.1574074 7.063712 0.1574074 7.0914125 0.14814815 7.132964 0.12962963 7.229917 0.10185185 7.3130193 0.06481481 7.354571 0.055555556 7.396122 0.027777778 7.437673 0.018518519 7.506925 -0.027777778 7.562327 -0.046296295 7.67313 -0.09259259 7.7146816 -0.12037037 7.770083 -0.1388889 7.8254848 -0.1574074 7.9085875 -0.21296297 7.9224377 -0.21296297 8.01939 -0.22222222 8.060942 -0.23148148 8.1163435 -0.23148148 8.144044 -0.23148148 8.1855955 -0.23148148 8.240997 -0.23148148 8.296399 -0.23148148 8.33795 -0.22222222 8.365651 -0.22222222 8.407202 -0.22222222 8.434903 -0.22222222 8.462604 -0.22222222 8.490305 -0.21296297 8.504155 -0.21296297 8.518005 -0.21296297 8.531856 -0.21296297 8.545707 -0.16666667 8.698061 -0.2037037 8.725761 -0.2037037 8.781163 -0.2037037
Demonstration
Your teacher will now demonstrate the use of the motion probe to work with velocity.

Look at the motion graph during the demonstration.






What do you see on the graph when your teacher moves in front of the probe? 1. Nothing changes. 2. Lines and dots jump around on the screen. 3. A line appears on the screen at the end of the movement. 4. A line is slowly drawn across the screen from left to right.
Your turn!

Set up your motion probe at the end of a desk or table. Click "STart" on the graph and move in front of the sensor several times while answering the following questions.





What is the velocity when standing at Station A?
What is the velocity when standing at Station B?
When is the velocity zero? 1. Only when standing close to the motion probe. 2. Only when standing away from the motion probe. 3. When moving toward the motion probe. 4. When not moving. 5. When moving away from the motion probe.

Was the velocity when going toward the motion probe positive or negative? 1. Positive. 2. Negative 3. I don't know. Was the velocity when going AWAY FROM the motion probe positive or negative? 1. Positive. 2. Negative. 3. I don't know.

NaN NaN 0.4553002 0.4402025 0.32425287 0.26349244 0.30682185 0.72293586 0.5933515 0.35908115 0.33737358 0.27488387 0.4938455 0.3236927 0.26555967 0.22919647 0.2537857 0.108843595 0.14415187 -0.3129895 -0.2849605 -0.5820083 -0.6913421 -0.37992096 -0.61810327 -0.36684316 -0.41995722 -0.52841294 -0.9380252 -0.89060724 -0.759349 -0.62579024 -0.49435562 -0.37310928 -0.26118416 -0.07529505 -0.046091985 0.04769723 0.28029537 0.27584085 0.31706536 0.37412626 0.2202254 0.40849137 0.5185509 0.5924485 0.5756825 0.5080235 0.456751 0.4179944 0.67001003 0.40091023 0.34361514 0.37159163 0.36312184 0.50858176 0.3347734 -0.02015926 0.06474715 2.932083E-4 0.09488318 -0.05188019 -0.1505896 -0.16402902 -0.0513715 0.042969987 0.1647783 -0.04926692 -0.15515254 0.2184174 0.10241026 -0.1838484 -0.06809263 -0.09876929 -0.017715685 -0.10241914 0.021495521 0.14280187 -0.09004982 -0.10983887 -0.058268636 -0.048761167 0.25730532 0.26903492 0.048393175 -0.13961881 -0.15166968 -0.19147255 -0.10346847 0.07635546 -0.4077213 -0.5676267 -1.0342324 -1.0149951 -0.79161763 -0.3728094 -0.32358766 -0.41622806 -0.50296813 -0.55068624 -0.5467838 -0.5108441 -0.51847863 -0.37890068 -0.18064196 -0.051379338 0.03479909 0.071095884 0.054015383 6.892793E-4 -0.003183999 0.046490707 0.036527224 0.041911546 -0.08682929 -0.28644216 0.0040742457 0.02398426 0.29089803 0.6310924 0.7694392 0.92749286 0.7436267 0.5732666 0.58234245 0.39996487 0.20674787 0.025661811 0.024268351 0.18077953 0.36004806 0.4253001 0.36551133 0.32901627 0.5391693 0.2934117 0.21665928 0.1625841 0.12804544 0.13005395 0.091700315
Your Train Trip
Now plan and make your train trip:
Measure and mark the two locations: Station A, 1.5 meters directly in front of the probe, and Station B, 0.5 meter in front of the probe.
Start at Station A, proceed to Station B, then return to Station A.
Start the graphing by clicking Start on the Velocity graph. Try this several times, until you have a graph that you are happy with and willing to share with the class. Then share the graph by clicking on the Submit button below the graph.


FLAG-N


Write any comments or questions in the space below.
Discussing class graphs
Have a look at the class's graphs on the next page. Please answer and discuss the following questions. You may change your answers after the class discussion.








Are the graphs all the same? What is similar about the graphs? What is different about the graphs? If you want everyone's graphs to match, what does everyone have to change or agree on?
Velocity and Position Graphs Together
At right are two graphs of a train trip, one is a graph of position and the other is a graph of velocity.
Station A is at position = .6 meters, and Station B is at position = 1.6 meters Answer the following questions:







What was the starting time of the trip FROM Station A TO Station B? This point is already labeled for you on the graph. What was the ending time of the trip FROM Station A to Station B? Label this point on the graph. What was the time taken going from A to B?


What is the change of position going from A to B? The average velocity is the change in position divided by the total time. Calculate the average velocity when going FROM Station A to Station B? (Can be a fraction or a decimal - you may use a calculator). Looking at the velocity graph during the trip from Station A to Station B, approximately what does it read?




OPTIONAL. Negative velocity calculations. Was the velocity for the return trip, from B to A, negative or positive? 1. Negative. 2. Positive 3. Not sure. Reading the velocity graph, what would you estimate is the average velocity during the trip from B to A? Was the change of position (final - initial) going from B to A positive or negative? 1. Positive. 2. Negative. 3. Not sure. Approximately what was the change in position? 1. Positive 2 meters 2. Positive 1 meter 3. Zero 4. Negative 1 meter 5 Negative 2 meters How much time did the trip from B to A take? 1. About 1 second 2. About 2 seconds 3. About 3 seconds


OPTIONAL: Calculate the average velocity for the trip from B back to A? (Average velocity = change of positive divided by amount of time taken)
0.637649 0.64434 0.647461 0.651344 0.655071 0.655296 0.653632 0.655522 0.646403 0.635742 0.641341 0.641948 0.648657 0.649766 0.649645 0.649281 0.651275 0.651795 0.652124 0.652159 0.651795 0.649975 0.653511 0.652592 0.655054 0.662248 0.668437 0.673429 0.679913 0.686552 0.696329 0.708898 0.717583 0.733271 0.746741 0.765221 0.779904 0.795766 0.814765 0.835013 0.856058 0.887383 0.909937 0.920927 0.93932 0.957107 0.98363 1.007657 1.01069 1.03099 1.056889 1.081887 1.109398 1.132975 1.15922 1.183785 1.211001 1.237733 1.275801 1.304526 1.341728 1.37756 1.406701 1.444267 1.461793 1.481677 1.495528 1.509899 1.517943 1.530078 1.539872 1.549251 1.550065 1.551175 1.550984 1.551417 1.551088 1.550083 1.551244 1.552562 1.551695 1.555543 1.556393 1.558802 1.560623 1.568597 1.568996 1.563154 1.562408 1.543044 1.530927 1.520196 1.505704 1.491333 1.479077 1.460008 1.443816 1.420864 1.406961 1.378912 1.346946 1.300574 1.268416 1.220744 1.180526 1.142648 1.106399 1.075404 1.041218 1.008523 0.976123 0.940863 0.91675 0.881004 0.855347 0.828061 0.801174 0.775535 0.749809 0.726268 0.70498 0.67967 0.658244 0.642971 0.630108 0.626624 0.618771 0.608855 0.601782 0.596599 0.593444 0.59119 0.588347 0.593097 0.596373 0.61357 0.618944 0.617436 0.61728 0.613137 0.613275 0.615962 0.61617 0.614194 0.613587 0.614472 0.614992 0.614714 0.613865 0.613119 0.613431 0.614159 0.613657 0.613397 0.613743 0.61331 0.61279 0.612062 0.611299 0.610866 0.610068 0.610519 0.610762 0.610883 0.611022 0.611264 0.611004 0.611212 0.611473 0.611663
New Questions and Investigations


Are there additional investigations you would be interested in doing?
Velocity Summary
"Velocity", (or "average velocity") is the "change of position" of an object, divided by the amount of time taken in moving.

The "change in position" of an object is its "ending position", minus its "starting position."

If your "starting position" is at position = 1.5 meters, and your "ending position" is at position = 3.5 meters, your "change of position" is
3.5m - 1.5m = 2 meters.

If that has taken you 4 seconds, your "average velocity" is 2 meters divided by 4 seconds,
2m / 4s = .5 meters per second.

If your "stating position" is at position = 3.5 meters and your "ending position" is at position = 1.5 meters, your "change of position" is 1.5m - 3.5m = -2 meters. (It is negative!)

If that has taken you 4 seconds, your 'average velocity" is -2 meters divided by 4 seconds,
-2m / 4s = -.5 meters per second. (It is negative, once again.)

While signed velocities are the mathematically best way to describe motion, students may be better off thinking (this is a quote from a 6th grader) "it's not really a negative velocity, it's just that it's in the other direction."