Unit 1 Summary Blog Post

    

What did I learn throughout this unit?

Throughout this unit, we have learned about position, slope, velocity, average velocity, distance, displacement, linear and parabolic graphs, intersections on graphs, as well as dependent and independent variables. With some explanation, these scientific terms are given a whole new meaning that is very relevant to our lives on a daily basis. Below I will define these terms and explain how they relate to physics and the modern world.


Constant Velocity Particle Model:

X = (V)(t) + Xo

This states that position = (velocity)(time) + starting position. This equation is often used in physics to help us estimate and calculate values on graphs.


Dependent/independent variables:

-x axis = independent variable (the variable we control as scientists) 

-y axis = dependent variable (the variable we measure)

Position: Position is where something is located. We use graphs and axes to give the position of something a number, although the number is only assigned to give a numerical explanation to where something is located. An example of this is where you are sitting right now, reading this blog. Although your "position" does not have a distinct numerical value, we can assign it one in order show where you are on a graph. Position on a graph is defines by the variable "X".


Velocity and Average Velocity: 

Velocity and average velocity have two different meanings. Velocity, how fast something is traveling at a certain point, can be shown through the slope of a graph. It is important to remember that when considering velocity, we must know that velocity can be negative or positive. Slope, measured by the equation (ΔY) / (ΔX) is equal to the velocity of an object. Average velocity, on the other hand, is shown by (Total change in X) / (time). Both Velocity and average velocity are depicted in the graph below. 

                                                               

In this graph, we can use the equation (ΔY) / (ΔX) to determine the velocity between six and eight seconds. in the graph, between the sixth and eighth seconds, the change in Y is -4m and the change in X is 2s. Thus, the velocity is -4m/2s which equals -2m/s. The average velocity on this graph is shown by (Total change in X) / (time). The graph both starts and ends at zero, giving us a total change in position of 0m. Our change in time was eight seconds. By plugging this in, we get 0/-8, which equals zero. The average velocity, although we moved, is still 0 on this graph due to the same starting and ending position. 



Distance and Displacement: 

Distance vs displacement can be depicted on the diagram to the right. Distance, or path route, is the total amount ground covered. For example, on the diagram on the right, you may have walked on a path through a park shown by the blue line. This path was 500m long, known as the distance. Although you have walked 500m on this path, you have only really traveled 250m from your starting point. You may have covered more ground to get there, but the direct route between start and end point was only 250m and is called displacement. Distance can be found by measuring the route an object took while displacement is measured by using the equation Displacement = X final - X initial (X final and initial being end and start points). 


Linear Graphs: 

Linear graphs are depicted by a straight line on a graph. These lines are very useful for having a visual depiction of data The two linear graphs that we use the most in physics are the velocity vs time graph and position vs time graph. Below are examples of both of these graphs and an explanation about each graph and the information they give us.



       

The velocity vs time graph on the left shows us

 how fast an object is moving at a particular 

time. These graphs are created with the equation 

Velocity = (Position) / (Time) For example,

in the graph above, the velocity is on the y-axis and 

the time is on the x-axis. Between zero and two

seconds, the object is moving at a velocity of 2m/s.

Then, for the  next two seconds it has a velocity of 

0m/s, a period of no movement. For the final two 

seconds, it has a velocity of -2 seconds, which means 

that it is traveling back toward the way it came.

         

Similarly, a position vs time graph shows us the 

position of an object after a certain amount of 

time.  These graphs are created with the equation 

Position  = (velocity)(time) + starting position. 

For example, the object starts at 0m but after 5s

it has reached 10m north of the origin. The linear

shape of the graph shows us that the object has

a constant velocity and allows us to predict values. 

Motion Maps:

Motion maps, a way to illustrate the relationship between time and velocity, are very helpful. Each second in a motion map is shown by a black dot and distance is shown by the axis that the motion map is plotted on. For example, in the motion map below, the object starts at 0m and then travels all the way to 6m in three seconds. It then pauses for two seconds and returns to the staring point in two seconds. From this motion map we can use the equation Change in position/time = velocity find the velocity of an object which for the first three seconds is 6m/3s = 2m/s.

Parabolic Graphs: 

Graphs that make a parabolic shape like the one depicted to the right have a variable that increases exponentially. This means that as one variable increases, the other increases at a rate that grows over time, creating a curved line. One example of this was in the rubber band lab. When we pulled the rubber band farther back, the distance it traveled grew exponentially. In order to use these graphs, we must change them into linear graphs. To do this, we must either square a variable or put a variable under 1 (1/X).

For example, in this graph we must square the x-axis variable in order to make it linear. Once we do this, the graph becomes linear and we can make predictions, but, we must remember to use the new variable X^2 in our equation.






Graph intersections: 

In our buggy lab, we learned that when two objects start away from each other and move towards each other at a constant velocity, we can predict intersection point from a graph as well as algebraically. The intersection point of the two lines is equal to the intersection of the two objects.

Equations: (buggy A) X = -30(t) + 200
                  (buggy B) X =  43.84(t) - 230 

Since we want the objects to have the same position (intersection), we set the equations equal to each other and get -30t+200 = 43.84 -230. By solving for t, we can get that the amount of time before an intersection would be 5.75 seconds. Since we are solving for position instead of time, we plug this time back in to the equation to solve for the position of the intersection. X = -30(5.75) + 200 which solves to be 27.6cm north of the origin, also represented by the intersection of the two lines on our graph.









Part B: Real Life Connections

In everyday life, we use velocity, intersection points, and the constant velocity particle model. Think about it, when meeting a friend by car, your meeting point is your intersection point. When predicting when we would meet, we are using a form of the intersections of two lines equation without knowing it. Also, when predicting how long it would get to school we use a form of the constant velocity particle model in order to predict how long it takes to go so far in a certain amount of time at a certain speed. Everyday we are using the connections we made in this unit without realizing it. After studying this unit, I am amazed at how common these ideas are in my daily life.