Tutor profile: Heather W.
The show Avatar: The Last Airbender will ALWAYS be know for its epic opening: "Water, Earth, Fire, AIR. Long ago, the four nations lived together in harmony. Then everything changed when the Fire Nation attacked...." Only YOU The CHEMISTRY AVATAR can explain how each of these "elements" pertains to the study of the chemistry of combustion. Ref for Avatar Quote: http://atla.avatarspirit.net/audio.php?id=2
First, let's talk about what the general definition of complete combustion is, chemically. Carbon-based item + oxygen ---> Carbon dioxide + water + ENERGY ENTER AVATAR STATE WATER: A byproduct of combustion (often seen as steam/part of smoke because of the level of heat!) EARTH: Earth things are carbon-based, and carbon-based items form the fuel for combustion like sticks and twigs. FIRE: That would be what we see as a physical form of HEAT and is usually the final form of a combustion reaction. AIR: There has to be oxygen for a reaction to proceed, and the byproducts are also part of air! Great classification, Avatar You! Your next task will be to bring the nations back into balance by balancing a combustion equation!
Imagine that (for science!!) your pupper is sitting in a wagon at the top of a large chunk of ice (representing the classic frictionless incline plane). You release your hold on the pupper's wagon, and it begins to roll down the ice plane. After 1 second, you measure the velocity and position of the wagon as your pupper happily rolls. The speed reads 2 m/s and the position reads 1 m. Since this is for science, you obviously need to record what happens to the speed and distance over 4 seconds of time. However, the pupper jumps out about halfway down, making the rest of your experiment a flop. Using your knowledge of the physical relationship between distance, acceleration, speed, and time, describe what you SHOULD have seen for the speed and distance at 0s, 1s, 2s, 3s, 4s.
Since this is "for Science!!", we first need to analyze & list the assumptions we are going to make. First off, we are assuming no friction/frictionless environment. It's specified in the problem, but as an FYI, if you see "ice" in a physics problem, you can go ahead and assume it's frictionless :) Since you didn't shove the wagon, you simply let go, the pupper is going to be experiencing constant acceleration. It's a fact that's a result of gravity. Now, let's see what we do know by making a list of the important things: time (s) distance (m) speed (m/s). I'll list them in sets with [brackets] to make it easier. So at the start, your pup was sitting still so, set one is... [0,0,0] Then, you were able to get a reading at t = 1s, so set two is... [1,1,2] Now, that's when the pupper jumped out, so the rest of our readings will have to be determined by MATH AND PHYSICS!! GASP. What do we know about the relationship between constant acceleration, time, velocity, and distance? We know... x = x0 + v0(t) + (1/2)at^2 and v = v0 + at At this point, we COULD plug in (t) into each equation and then get some numbers... but we are missing a KEY feature... the acceleration 0_0. However, we can draw some general relationships here because we know that the acceleration is constant. The position is dependent, at its core, on time squared. Speed increases as time increases, also at a constant rate. We can see and know this a bit easier by thinking of the velocity equation as a linear equation and the position equation as a quadratic equation. So at t =2, we should have seen [2,4,4]. The distance is represented by time^2, and 2^2 = 4. The velocity is a little trickier to figure out... we know that the speed increases with time at a constant rate. Well, what is the rate? It's 2 m/s, because that's the slope of the line. So for every second, we will see an INCREASE by 2 m/s. 2 + 2 = 4 m/s. At t = 3, we should have seen [3,9,6]. Distance: 3^2 = 9m. Velocity: 4 m/s + 2 m/s=6 m/s and at t = 4, we should have had [4,16,8]. Distance: 4^2 = 16. Velocity: 6 m/s + 2 m/s = 8 m/s So, the final set of pairs reported as [time (s), distance (m), velocity (m/s)] [0,0,0] [1,1,2] [2,4,4] [3,9,6] [4,16,8]
[Slope Intercept Form/Calculating Slope] I am using Google Maps to map out the fastest route between two Pokemon Go gyms. This route happens to be a straight line AND on the cartesian plane (amazing!!). If Gym A is at (0,1) and Gym B is at (2,4), what is the slope-intercept form equation describing the straight (linear) path I will take between Gym A and Gym B?
Let's start out by re-stating what we know. It will help if you draw a picture! My two points of interest: Gym A (0,1) and Gym B (2,5) My type of line: Straight/Linear My general slope-intercept formula: y=mx+b where m = slope and b = the y-intercept point. Go ahead and look at your picture. It's going to be easiest to solve for "b" first in this problem. When we draw the picture of these two points, you'll see that Gym A is actually ON the y-axis at point 1, so it IS the y-intercept point! Now line formula looks like this: y = mx + 1 Let's solve for slope now or "m" The general equation for slope is m = (y2-y1)/(x2-x1). You may have seen this represented as m = Δy/Δx or said as "slope equals the change in y over the change in x". There are some other forms you may have heard it in, but they should all give you the same answer in the end! Since I'm traveling from Gym A to Gym B, we are going to designate Gym A (0,1) as our "1" point, so its x and y will represent x1 and y1. Gym B's coordinate (2,5) will give us x2 and y2. Let's set up the formula: m = (y2-y1)/(x2-x1) = (5-1)/(2-0) = 2 Now we have all the pieces to show our *finished* slope-intercept form equation that will describe the path I'm going to walk to get from Gym A to Gym B in Pokemon Go! y = 2x + 1 Great Job!
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