Unit One Summary - So Many Graphs!
Independent: The one over which the experimenter has complete control - The X-Axis
Dependent: The one that responds to changes in the independent variable - The Y-Axis
These variables could then be expressed in a mathematical expression. For example, this graph as the X axis and Y axis labeled according to the independent and dependent variables. I can create a mathematical expression by observing the slope and y-intercept.
In the expression, the x and y are replaced with the units being observed. In Example set 1, we are observing Mass in kg and Volume in m3.
So, taking the information we have, we can create an expression.
Slope = 122.99
Y - intercept = 0.0208
Mass (kg) = 122.99(m3) + 0.0208
We continued our studies by learning about graphical methods which match an equation to a curve. This is called curve fitting. When graphing a curved equation, the data can be modified to create a linear equation.
y = m(1/x) + b : As x increases, y decreases - y is inversely proportional to x
y = mx^2 + b : Y is proportional to the square of x
y^2 = mx + b : The square of y is proportional to x
Next, we moved from distance vs time graphs to motion maps. A motion map represents the position, velocity, and acceleration of an object at equally spaced times. The position of the object is represented with a dot. The arrows signify the object's velocity.
If the object is moving quickly, the vectors (arrows) will be longer and the points will be spread further apart. The direction of the vectors changes depending on the direction of the moving object. Left-facing arrows indicate backwards movement while right-facing arrows indicate forward movement. A halt in movement or stopping point can be represented with multiple dots without an attached vector. Each dot represents the unit of time in which the object remained stationary. Finally, multiple objects can also be represented with multiple dot-vector sequences on the same motion map.
The last graph we learned about is the velocity vs time graph. This represents the velocity of the object in relation to the time it traveled.
The y - axis contains the velocity while the x - axis measures the time. The line mapping an object's travel will change depending upon the object's activity.
For example, this graph represents an object that begins traveling forward at an increasing velocity. It remains steady for two seconds before declining velocity quickly and reversing directions. It increases velocity once more before reversing back to a forward direction.
Often these graphs are compared with each other. They can express the same information by comparing different variables of data.
All of theses graphs can be represented with algebraic equations.
Velocity: - Change in Position/Time
- Rise/Run
- Change in x/Change in y
Constant Velocity Particle Model: x = vt + xo
X = The position of an object at any instant in time
V = The velocity of the object
T = Time
Xo = The initial position of the object at t = 0
A lot of my connections came from the labs conducted during class. For example, the Texting While Driving lab. We ran a multitude of tests to prove how dangerous texting while driving is. This genre of research produces important statistics to be considered during our everyday lives.
Also, a large majority of my math class, F2S, involves plotting on Excel and using very similar - almost identical concepts. We consider independent and dependent variables and use the equation
y = mx + b extensively. With physics, it is much easier to make a connection between math and science, bringing skills from one class into the other.
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