![]() To linearize a nonlinear function, we need to find a straight line that is a good approximation of the function. ![]() Nonlinear functions can take many different shapes, including curves, loops, and jumps. Here are some key points to consider when linearizing a graph:Ī linear function is defined by a straight line, which can be represented by the equation y = mx + b, where m is the slope and b is the y-intercept.Ī nonlinear function is any function that is not a straight line. ![]() This can be useful for making predictions or understanding the general trend of the function. Linearization of a graph is a method of approximating the behavior of a nonlinear function with a straight line. We also reviewed how to interpret these graphs, but it is imperative to understand the relationships each graph has to one another. Graphical Representations of MotionĪs we covered in 1.1 Position, Velocity and Acceleration there are ways to represent all three quantities graphically. The acceleration is equal to the rate of change of velocity with time, and velocity is equal to the rate of change of position with time. The linear motion of a system can be described by the displacement, velocity, and acceleration of its center of mass. ⟶ A force may be applied to this point to cause a linear acceleration without angular acceleration occurring. Key Vocabulary: Center of mass - a point on an object or system that is the mean position of the matter. The acceleration of the center of mass of a system is related to the net force exerted on the system, where a = F/m. Overall, different representations of motion can be used to help understand the characteristics and behavior of moving objects, and can be useful tools for predicting and analyzing the motion of objects in different situations. These representations can help visualize and understand the motion of an object. These equations may involve variables such as position, velocity, and acceleration, and can be used to make predictions about the motion of an object.ĭiagrammatic representations: These include sketches or diagrams that show the position, velocity, and acceleration of an object at different times. These data may include position, velocity, and acceleration at different times.Īnalytical representations: These include mathematical equations that describe the motion of an object. Numerical representations: These include tables or lists of numerical data that describe the motion of an object. ![]() These graphs can be used to represent the motion of an object and to understand its characteristics, such as its speed and acceleration. Graphical representations: These include position-time graphs, velocity-time graphs, and acceleration-time graphs. Some common types of representations include: In AP Physics 1, we study different representations of motion to understand and analyze the movement of objects. ![]()
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