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  2. Motion graphs and derivatives - Wikipedia

    en.wikipedia.org/wiki/Motion_graphs_and_derivatives

    Motion graphs and derivatives. The green line shows the slope of the velocity-time graph at the particular point where the two lines touch. Its slope is the acceleration at that point. In mechanics, the derivative of the position vs. time graph of an object is equal to the velocity of the object. In the International System of Units, the ...

  3. Fourth, fifth, and sixth derivatives of position - Wikipedia

    en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth...

    Time-derivatives of position. In physics, the fourth, fifth and sixth derivatives of position are defined as derivatives of the position vector with respect to time – with the first, second, and third derivatives being velocity, acceleration, and jerk, respectively. The higher-order derivatives are less common than the first three; [ 1 ][ 2 ...

  4. Equations of motion - Wikipedia

    en.wikipedia.org/wiki/Equations_of_motion

    To state this formally, in general an equation of motion M is a function of the position r of the object, its velocity (the first time derivative of r, v = ⁠dr dt⁠), and its acceleration (the second derivative of r, a = ⁠d2r dt2⁠), and time t. Euclidean vectors in 3D are denoted throughout in bold.

  5. Second derivative - Wikipedia

    en.wikipedia.org/wiki/Second_derivative

    In calculus, the second derivative, or the second-order derivative, of a function f is the derivative of the derivative of f. Informally, the second derivative can be phrased as "the rate of change of the rate of change"; for example, the second derivative of the position of an object with respect to time is the instantaneous acceleration of ...

  6. Generalized coordinates - Wikipedia

    en.wikipedia.org/wiki/Generalized_coordinates

    In analytical mechanics, generalized coordinates are a set of parameters used to represent the state of a system in a configuration space. These parameters must uniquely define the configuration of the system relative to a reference state. [1] The generalized velocities are the time derivatives of the generalized coordinates of the system.

  7. Linear motion - Wikipedia

    en.wikipedia.org/wiki/Linear_motion

    The motion of a particle (a point-like object) along a line can be described by its position , which varies with (time). An example of linear motion is an athlete running a 100-meter dash along a straight track. [2] Linear motion is the most basic of all motion. According to Newton's first law of motion, objects that do not experience any net ...

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