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Learn about linear motion, one-dimensional motion along a straight line, and its related concepts such as displacement, velocity, acceleration, and jerk. See the equations of motion for constant acceleration and their graphical representations.
In SI, this slope or derivative is expressed in the units of meters per second per second (/, usually termed "meters per second-squared"). Since the velocity of the object is the derivative of the position graph, the area under the line in the velocity vs. time graph is the displacement of the object. (Velocity is on the y-axis and time on the ...
Learn about the equations that describe the behavior of a physical system in terms of its motion as a function of time. Find out the types, history and applications of kinematics and dynamics, and the SUVAT equations for constant acceleration.
A derivative is a tool that quantifies the sensitivity of change of a function's output with respect to its input. Learn how to define, notate, and calculate derivatives of functions of one or several variables, and see their applications in physics and calculus.
The superposition principle states that the net response of a linear system to two or more stimuli is the sum of the responses to each stimulus individually. This principle applies to many physical systems and phenomena, such as waves, algebraic equations, and Fourier analysis.
Lagrangian mechanics is a formulation of classical mechanics based on the principle of least action, introduced by Joseph-Louis Lagrange. It describes a mechanical system as a pair of a configuration space and a Lagrangian function, and derives the equations of motion using Lagrange's equations.
The gradient of a scalar function is a vector field that points in the direction of fastest increase of the function. Learn how to calculate the gradient using partial derivatives, the nabla operator and different coordinate systems, and see applications in optimization and physics.
The second derivative of a function is the derivative of its first derivative, and it measures the rate of change of the rate of change. It can be used to determine the concavity, inflection points, and local extrema of the function, as well as to approximate quadratic functions and eigenvalues.