> TVSq` >bjbjqPqP M::000D,,,,@tD["EEE!!!!!!!$Q#h%|!]0n|Enn!"n@80!n!0&5Qp,@& l+"0["5&5&5&0,E^'LsEEE!!EEE["nnnnDDDdDDDDDDMark Roy
Fort Washakie Middle School
90 Ethete Road
Ft. Washakie, WY
HYPERLINK "mailto:mroy@fremont21.k12.wy.us" mroy@fremont21.k12.wy.us
High Velocity Teacher
Middle School Science topic: Kinematics
Materials: 4 stop watches, 50-meter tape, track or 30 meter long space where student can run and teacher can walk, Ti 84 Plus calculator
Objective: Students will observe, physically and mathematically, the difference between a scalar quantity (speed) and a vector quantity (velocity) and make complex time and distance measurements of a runner and a walker and graph the motion of each.
Having developed abilities to manipulate the equation Speed = Position (Pf PI)/ Time and to produce position/time graphs on paper and with a TI-84 Plus calculator, students are now presented with a challenge from the teacher. I can walk 30 meters faster than the fastest of you can run the same distance.
Instructions: The student with the fastest time in the class will run a 30-meter ladder. Timers will be stationed at 0m, 10m, 20m and 30m. Each time the runner touches or crosses your position you will mark and record the time. That means that the timer at 0 meters will record 2 times, the 10-meter timer will record 4 times, the 20-meter timer will record 2 times and the 30-meter timer will record 1 time. You will then record my time walking 30 meters. Oh yea, I will be walking 30 meters without doing the ladder. Lets go!
Now that we have all this data lets organize it into a data table.
Position in meters for running studentTime in seconds for running studentPosition in meters for TeacherTime in seconds for Teacher0 m0 s0 m0 s10 m10 m0 m20 m10 m30 m20 m10 m0 m10 m20 m30 m
Now its time to do some calculations and see who is fastest. But first, we need to introduce a few new physics definitions for motion. Please add these to your vocabulary lists.
Scalar quantity- is a measurement of magnitude only. Speed, distance, mass and temperature are scalar quantities.
Magnitude- is simply how much of something there is.
Vector quantity- is a measurement that includes both magnitude and direction. Displacement, velocity and acceleration are vector quantities.
Average velocity- is displacement divided by change in time. V = D (PF PI)/ T
Notice that displacement is a vector quantity so direction is part of that measurement. That means if you run one direction and then turn and run another way you must include that change as you calculate the magnitude of your displacement. So the calculation of the displacement of the student runner we would be 0m+10m-10m+20m-20m+30m = 30meters. The change in time is TF TI = T.
Please calculate the student runner s average velocity and mine and compare them. Who was faster?
There are two sides to every story so lets look at instantaneous velocity, at least as instantaneous as we can get using the data we have. Calculate the velocity between 0m and 10 m for the student runner and me walking. Who was faster? Do the calculations for 10 to 20 meters and 20 to 30 meters. Did I win any part of the race?
Now lets see if we can describe the student runners motion graphically. Sketch what you think a position/time graph will look like below.
Now follow these instructions to graph the data on your TI-84 Plus calculator.
Turn on your calculator. Press ` + and select ClrAllLists. Press e. Press the S key and select EDIT. You should have a screen that looks like this:
Use the scroll arrows to highlight L2 and type in the positions starting at 0m.
Use the left scroll arrow to move the curser to the L1 column and Type all the times in L1 starting at 0. Make sure you have a time that matches up with each position. If you are missing a time place the calculator curser on the timeless posEFstuX a |
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Now press ` !. Press 1 to select Plot 1. Use the scroll arrows to highlight On and press e. Use the scroll arrows and e key to set the screen to look like this:
Press the @ key to set the intervals and ranges of your graph. Enter the values shown. You will have to determine the correct Xmax according to your data. (Hint: What was the student runners final time ?)
Press %
Does the graph look like what you sketched above? If so show the teacher and prove he isnt so high velocity! If not, consult with your lab group and try again and then ask the teacher for help if you need it.
If you finish early try making distance vs time graphs that will show average velocities for the student runner and Teacher walking.
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