Another Worksheet... Darn

Hello everyone out there listening, or I guess reading, if you want to get technical.  This week, just like the last one, I had to miss class.  You can blame my orthodontist for this one, but of course, missing class meant missing another discussion, and I really don't like missing discussions.  I mean, those things contain some valuable information which now, because of my appointment, I will never know.  Really, all I took out of this week was a fairly easy fiesta (quiz) and a worksheet.

Fiesta

You all know how it is.  When you think something is easy, you usually end up doing horrible, especially in a class like math.  However, I seemed to understand the fiesta.  After all, it was on Position vs. Time graphs which are easier for me to comprehend anyway, so overall I think I did pretty good.  I've got my fingers crossed.

Worksheet

The worksheet was called Constant Velocity Model Worksheet 4: Velocity vs. Time Graphs and Displacement.  We were told to do the worksheet with our tables and discuss any questions we had. Again, like the fiesta, I didn't find this to be too hard, and I found it very helpful to work and discuss in a group.

Basically, the worksheet went through making motion maps, writing written descriptions of the motion of objects, making Position vs. Time graphs, making Velocity vs. Time graphs, writing mathematical expressions for motion, and determining displacement.  However, there were three other things which still kind of have me confused; the area under the curve, average velocity, and average speed.

The Area Under the Curve

The only reason I understood this part of the worksheet was because I had actually watched a video on my own about it.  The area under the curve is basically the area of the "squares," I guess, on a Velocity vs. Time graph.  You would basically do length times width or base times height or side times side (whichever you prefer) to get the area of each little rectangle, and then you would add them all together to find the total area under the curve.  Supposedly, this comes out to the displacement of the object, so this could actually be quite a handy way to find it.

The graph above is actually the Velocity vs. Time graph from the worksheet.  If you notice, there are three rectangles, and if you were to find the area of those and add them, then you would find the total displacement.

If you were wondering what you do for the "non-rectangle" parts, you basically do nothing. Technically, you would find the area of them too, but since it isn't a rectangle, it only has one dimension, so its area is technically 0.  Basically, there is no need to find it because it is always 0.

Average Velocity

For this one, I must thank my group for helping me figure it out.  To find average velocity, you first need to know what velocity is.

Velocity is basically speed with direction included.  This hints that velocity can be negative.  If you used the graph above, and you were asked to find the average velocity form t=4 to t=8, you could do so easily.

All you do is take the firs velocity at t=4, which happens to be 3 meters/second, and add the velocity at t=8 which is -5 meters/second. So, 3+(-5)= -2 meters/second.

You would then divide by the amount of time passing to get the average.  This comes out to be 4 seconds, so you would do -2/4 which is equal to-1/2 meters/second.

Average Speed

Again, I must thank my group for helping me figure this out.  However, we still aren't 100% positive on this one, so I may be wrong in what I am saying.  To find average speed, you need to know what speed is.

Speed is distance divided by time.  There is no mention of direction in the definition, so we know that speed cannot be negative. 

If you were asked to find the average speed from t=4 to t=8, you would take the two velocities mentioned before and make them positive.  You would get 3+5=8 meters/second, and you would then divide by 4 to get 2 meters/second.

Reflection

Again, I am not positive on the average speed portion of this worksheet, but I am fairly certain about the other parts.  Truthfully, I wish that I hadn't missed two days of class.  It really makes me feel behind, but I guess I have to embrace the confusion like they always say.  I hope that I can get back on track next class. Although, I know for sure that all I can do is try my best.