Two weeks of FUN

     Hey everybody, I'm back. I know I didn't post a blog last week, but I wanted to try something new, instead of writing a blog every week and have some topics run into the next week, I wanted to try and blog after a new concept is completed, also, writing a 4 page blog takes up a ton of time, which I wanted to myself for once. Anyways, the last two weeks we have been continuing our focus with motion maps, mathematical equations, and a bunch of other graphs that show velocity, position, and time. These are all good and well, but the main things that caught my eye was the explanation of average velocity, average speed, displacement, and interpretation of some graphs. This is because I have sooooo many issues with these concepts (or at least I used to).
     To begin with, on the first day of the first week we had a long discussion on what is displacement. You see, our leading theory the week before was how far an object moved between two points in a given amount of time. However, this theory thrown out the window as soon as we started class. It turns out one of my classmates had a different view of what it was and moved right to that theory. The person's theory stated that displacement is no more than how far an object moves in relationship to the starting point, which did make a little sense, especially, when put into context with the packet we had earlier. The packet defined displacement as "final position minus the starting position". Even though we came to the right answer I was a little angry. This is because not only did we skip over a viable theory (the one I had long supported also) and despite 30 minutes of raising my hand, we never took a second look at that theory. It wasn't until after 45 minutes that my quest was completed and I had closure. Also, I wasn't the only kid who had a problem with not being called on, I know of at least 2 other kids who could not have their voice's heard. It did however, get better. This is because Mr. B. intervened on our behalf a couple of times. I think the plus- delta we had is doing wonders.
     After that, there was the average speed and average velocity equations I could not remember to save my soul and when I read them it was like reading gibberish. The actual equations were written as " average velocity is the displacement (final position minus original position) divided by the time elapsed" and average speed was " the distance traveled along the path (change in odometer reading) divided by the time elapsed". The only thing I could get out of those definitions was the fact that the denominator was how much time went by. It wasn't until we had two packets that I finally understood what to do. It turns out with average velocity you just divide displacement by the time elapsed. This was easier for me to remember, but there was another way of solving average velocity also. It involved connecting the two points directly and finding the slope. That was my initial guess as to how to do this equation, but I was not sure. As for average speed, it involved counting up all of the distances period, and then divide it by the amount of time that had passed. There was one other caveat though, there is no such thing as a negative speed so if we had a negative speed we would use the absolute value. These two conversations took up the entire time in the first week.
     In the next week we talked about interpreting position vs. time graphs, motion maps, and velocity vs. time graphs. This was done in the form of another packet (which I forgot we had). Even though I forgot to do that packet I was able to have my voice heard, this was also due to the fact that we implemented the hand raising system for talking.
    The first thing we talked about was the position vs. time graph. This started out with us drawing the graph to replicate the movement of a skater. Now, all of the class drew a standard graph with sharp curves and straight lines because we assumed that was how the skater skated based on the data. However, Mr. B. pointed us in the direction of other possibilities, like curved lines instead of straight ones, also a gradually decreasing speed when the skater stop not a sudden drop. This led to a lot of confusion, especially when we tried to translate all of the possibilities. For instance, when we had a curved line between the points we said that the skater was gaining speed and for the sharp drops the skater tripped and fell, but in the end our original design was correct.
    After that side note we started to talk about the infamous motion maps. Now, I say infamous because all of us hate these maps because almost no one really understands them. Some of the things that we talked about this time pertained to one map in particular, it is is shown on the right.
The question was how many seconds can we actually count. Half of the class said 3 seconds and the other half said 4. The argument for 3 seconds was the fact that there were only 3 complete cycles of a dot followed by an
arrow ending with another dot. Then, the argument for being able to tell 4 seconds was the fact that it is the arrow that tell the object's speed and duration of travel, therefore, since we had the arrow and it was a constant length we could assume the next point would follow the same pattern as previously produced. I supported that theory until the bitter end, it turns out we could tell only three seconds because the speed or duration of the skater could have changed with in the data down the road. This discussion did however, bring spark
my question of "if we can't assume the point of the next cycle then what do we do with that line?" This question was not answered this week, but Mr. B. heard it and really liked it, so it will be asked next time. Some other questions that I would like to ask include "what do each part of the motion map represent, like the arrow or line" or "why don't we use lines or segments instead of rays". My guesses for these questions in order are, 1. it doesn't represent anything, 2. the arrow represents the graph continuing and the line is how fast  the object is moving, and 3. we use a ray in order to represent the starting and ending of a period.
    After that, we talked about whether each point represents a second or just a snap shot of time, along with what can do with that information. We did this by using the moving model again. Mr. B walked along a marked path dropping bean bags at even intervals of time to represent the points of the map. This showed that each point does represent a snap shot in time. That was my original guess, too. Next, was the realization that on any type of graph speed or velocity cannot be found without 2 or more points. This went back to the comment of the slope being the speed of the an object.This was more of a statement by Mr. B than anything.
     After that, we discussed what the area in between the axis and line meant on a velocity vs. time graph. We first had to find out what each box meant, and that wasn't hard. We just had to do a little cross multiplying and we were done. Each box (for our graphs) represented one meter. We did however, learn something to be aware of, it was to make sure that we actually multiplied and not set up my equations as if we were dividing. From there, we counted the number of boxes between those two lines and that apparently represented the displacement of the object too.
     Next, we briefly touched on relations again, specifically on whether we should name a velocity vs. time graph with a horizontal line as "no relationship". This issue was again a split right down the middle of the class. Some were saying that there was no relationship based on our previous discussions from week 1 and 2. However, the actual question was to write the mathematical equation that represents that set up. Then, the other half of the class remembered that for a horizontal equation it is just y= a number. We resolved the issue by just putting both forms and say that it's a matter of preference.

     Finally, we talked about how all of these graphs are interconnected. We talked about how we could take any of the representations of movement we learned i.e. the position vs. time graph, velocity vs. time graph, motion map, description of the event, or a motion map and make all of the others. In fact, that is what our homework is on, we have to create the other 4 representations for the one representation that is given to us. Later in the future Mr. B. said we will be getting into some of the laws pertaining to motion, so that will be fun.
    
Here are some helpful sources if there is still any confusion on any of the topics I discussed
http://www.physicsclassroom.com/class/1dkin/u1l4e.cfm
http://www.physicsclassroom.com/class/1dkin/u1l1d.cfm
https://www.youtube.com/watch?v=gC0hlJlbu1A