In the graphical analysis module, we wish to develop the concepts and tools necessary to interpret and analyze graphs containing information about position, velocity, acceleration, as a function of time. The graphs we will analyze all contain information about the motion of an object. Through the use of these graph, a foundation for a deeper understanding of the underlying physics can be obtained.
This short video lets you connect position, velocity, and acceleration graphs to a cars motion.
kinematics
Read the BoxSand Introduction and watch the pre-lecture videos before doing the pre-lecture homework or attending class. If you have time, or would like more preparation, please read the OpenStax textbook and/or try the fundamental examples provided below.
Understanding motion can be accomplished through the aid of interpreting plots of data. Plots of motion data show how the physical quantities observed change in time. The 3 quantities usually plotted are position, velocity, and acceleration. When plotted these quantities are shown as functions of time, meaning that on the y-axes will be the physical quantity measured, on the x-axes will be time, and the line on the graph shows how that quantity changes in time.
Often in the real life situations the device used to measure features of motion only records one type of physical quantity – an example being if you recorded the velocity of your car as a function of time with the aid of its speedometer. You would like to understand how to use that data to determine other physical quantities, such as your position or acceleration as a function of time.
To go between plots of position, velocity, and acceleration requires two main abilities, determining slopes of plot lines (sometimes curved) and area under the plot lines. There are simple connections between the various plots which can be summarized by the following picture. Clicking on each of the arrows will show you how you can convert from one physical quantity to the next and back again.
Graphical Analysis Infographic
Area of a rectangle
ARectangle = Length x Width
Area of a Triangle
ATriangle = 1/2 x Base x Height
Now, check out the pre-lecture reading and videos below for more information on Graphical Analysis
This link takes you to the graphical analysis of kinematics section of the openstax college physics textbook.
