New Providence Science Department

New Providence Science Department

Physics Summer Reading Assignment

In the first few weeks of all 11th grade physics courses, teachers will be discussing some of the important ideas about graphing, the types of graphs and graphical calculations. In order to start developing an understanding of this topic, students entering eleventh grade are required, as part of their summer reading, to read and understand the passage below.

Students will be asked to discuss their general understanding of the content of this text in the first few days of the school year and will be then assessed on their individual understanding and ability to perform graphing calculations.

Reading Standards for Literacy in Science and Technical Subjects 11-12

2. Determine the central ideas or conclusions of a text and summarize the complex concepts.

4. Determine the meanings of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 11-12 texts and topic.

10. By the end of grade 12, read and comprehend science/technical texts in the grades 11-12 CCR text complexity band independently and proficiently.

Properties of Graphs

Axes

When examining an x vs. y graph of any set of data, it is important to look at what data was actually collected. This information can be found on the axes of a graph along with the units that the data was measured in. The two axes are x and y. The x-axis is the horizontal axis while the y-axis is the vertical axis. The x-axis will always contain the data for the variable we are changing; independent variable (usually time). While the y-axis will show data that is dependent upon our x-axis variable. An example would be a position vs. time graph. We would normally plot time on the x-axis and position on the y-axis. We do this because time is allowed to move and can take on 1, 2, 3, or any number of seconds. But, where the object is at any point in time, its position, is dependent on what time we choose.

Also, along with what data was collected, the units for that data can also be found on the axes of a graph. It is important to note the units of a graph, because the units will help guide us to other quantities we can measure. The scale of the graph is important for knowing the range of units that we are working with and the range we should get for a calculation we can make based on the graph.

Types of Graphs

There are several different types of graphs that can be studied. One type is where as the independent variable changes, increases or deceases, the dependent variable changes the same way. The simplest way for this to happen is in a linear pattern. The points connect to make a straight line whenever the x-data and y-data increase or decrease by the same amount between each number. The simplest example of a graph that would look like this is y = x.

Another type of graph where both variables change the same way is a graph of a square function. Square functions occur when the x-data changes by the same amount between each number, but the y-data changes by the some amount each time squared. The simplest example of a graph that would look like this is the graph of y = x2.

The other type of relationship among x and y is that if x does one thing y will do the opposite. This is called an inverse function. That means as x increases, y will decrease or vice versa. The simplest for of this function is y = 1/x.

Like a linear relationship, there was also a parabolic relationship, for an inverse relationship there is also an inverse squared relationship. This can be explained that as x changes one way by some number, y will change oppositely by some number squared. The simplest form of this graph is y = 1/x2.

Linear / Square / Inverse / Inverse Squared

Graph Calculations

Slope

Perhaps the most basic calculation that can be performed on a graph is determining its slope. Many quantities in physics are determined by finding slope of a graph. Velocity, The slope represents the change of the y-axis compared to the x-axis. The slope can be positive, negative, and zero and can be calculated using the following formula.

Since the slope is calculated using division, the units for slope calculations will always be of the form “y-axis per x-axis”. For the graph shown the slope would be:

Area

Area calculations refer to the area of the shape created by the line or curve and the x-axis. The area represents the result of multiplying the x-axis and the y-axis (the order does not matter). It is calculated by determining the shape created and applying the appropriate area formula. Since area is calculated by multiplication, the units for area calculations will always be of the form “y-axis times x-axis OR x-axis times y-axis”.