Unit 2 - Constant Velocity

Unit notes here.

-Idea: Give lab practicum challenges at the beginning of units, but do them at the end. This unit is a t-bone crash between two different buggies.

-Buggy paradigm lab (to start learning something in the unit)

• Run the buggy and list student observations about it. 
• Is there anything on this list that is uncertain? Can we verify that the speed is constant?
• How do we measure speed? (can't do it directly) What can we measure? (d and t)
• Have each group do the same part one, and then a different part 2 (make sure original starting line important as "zero"):
• start at negative position and move toward zero
• start at end point and head back to zero (with same car or with different car)
• start at zero and head the opposite (negative) direction
• Start at a certain distance and still go forward
• Start at the same place but with a different speed car
• Opposite direction with a different speed car
• Each group has 2 data tables, and drawings to show what they did, but both lines on the same position vs. time graph and later add a velocity vs. time graph.
• Did we all do the same part 1? Tell me about it… 
• What does this graph tell you?
• What's the same/different from part 2? 
• What does the same distance from zero positive or negative mean?
• Tell us about the distance each went in the same amount of time, say 5 seconds
• What does the y-intercept mean?
• How does the slope/steepness of the lines compare?
• Is a constant speed also supported by the data table?
• Can we agree that we will call to the right positive and towards the left negative?
• Summary: Slope of the line = velocity of the car and a straight line means it was a constant speed

 

-Unit 2 Worksheet 1 - Constant velocity on position vs. time graphs. Students must do the worksheets on their own- don't help others- that hurts them in this case.

-Unit 2 Worksheet 2 - Constant velocity with velocity vs. time graphs. Conclusions from worksheets 1-2:

• The slope = velocity = d/t (rise/run)
• Equation of the line is y=mx+b, where the y-axis is position, the slope (m) is the velocity, the x-axis it time, and y-intercept (b) is the position at time zero. Therefore, d=Vt+do (do being the position at time zero). 
• So the change is distance = v*t
• Problem #7- the displacement is the change in the position (final position - position at time zero)
• Problem #5-7- Shade in 1 sec between your line and the horizontal axis on #5. Could we find the area of that? Did it move 1 m in 1 sec? Try it with the other times. 
• On a velocity graph, area = b*h = s*m/s = m, which matches displacement = v*t. The area between the line and the horizontal axis = the displacement. 

-Add in a pictoral model - motion maps. 

• Flash lights on and off to beat/metronome or open/close eyes and run buggy
• Lights off, "Ah, I don't know where the car is…"
• Lights on, "Ah, where'd it go? Oh, it's way over there…"
• Draw a ruler on the board. What would be easier to draw every second to show where the car was? (a dot) Always draw the dots first. 
• What can you tell me about the dots? What does the spacing indicate? 
• Now run the car the opposite direction. How can I show this differently? (draw arrows random sizes) What's wrong?
• Why should the arrows be the same size?
• What do the arrows represent? both speed (magnitude) and direction -> velocity 
• What do the dots represent? The dots must show the position and time- where the car is every second. This means 5 dots on a motion maps means 4 seconds, because the first dot is time zero.
• Run a faster/slower car. How would this look different? Draw it. 
• Make a d vs. t data table, d vs. t graph, x vs. t graph, and v vs. time graph to match both motion maps. 

-Constant velocity deployment unit work:

• Tips- select certain questions appropriate for each group and do not point things out to students. They need to come up with the ah-ha moment themselves. 
• Unit 2 Worksheet 3 
• Reading- motion maps
• Unit 2 Worksheet 4 - Constant velocity with all motion representations 

• Unit 2 Worksheet 5 - Constant velocity stacks of motion representations

-Lab Practicum: 2 Buggies T-bone Crash

• Both buggies must start at least 2 meters away from the crash point. You may only have one buggy running at a time, and you must stay off the crash course until it's your turn to go. (Can limit students by making them release it at the same time or not allowing a stopwatch during the test so they have to calculate the distance.)
• Alternate idea: Do a head on crash from a certain distance and they have to put the x where they the buggies will crash. 
• On their whiteboards, student must show work- d vs. t and v vs. time graphs with displacement on both graphs and a motion map 
• Great time to introduce using motion detectors to test the speed of both cars- show how to get both graphs and slopes and equations