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

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

    Snap, [6] or jounce, [2] is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. [4] Equivalently, it is the second derivative of acceleration or the third derivative of velocity, and is defined by any of the following equivalent expressions: = ȷ = = =.

  3. Motion graphs and derivatives - Wikipedia

    en.wikipedia.org/wiki/Motion_graphs_and_derivatives

    Since acceleration differentiates the expression involving position, it can be rewritten as a second derivative with respect to time: a = d 2 s d t 2 . {\displaystyle a={\frac {d^{2}s}{dt^{2}}}.} Since, for the purposes of mechanics such as this, integration is the opposite of differentiation, it is also possible to express position as a ...

  4. Time derivative - Wikipedia

    en.wikipedia.org/wiki/Time_derivative

    Many other fundamental quantities in science are time derivatives of one another: force is the time derivative of momentum; power is the time derivative of energy; electric current is the time derivative of electric charge; and so on. A common occurrence in physics is the time derivative of a vector, such as velocity or displacement. In dealing ...

  5. Derivative - Wikipedia

    en.wikipedia.org/wiki/Derivative

    The higher order derivatives can be applied in physics; for example, while the first derivative of the position of a moving object with respect to time is the object's velocity, how the position changes as time advances, the second derivative is the object's acceleration, how the velocity changes as time advances. Derivatives can be generalized ...

  6. Second derivative - Wikipedia

    en.wikipedia.org/wiki/Second_derivative

    The last expression is the second derivative of position (x) with respect to time. On the graph of a function, the second derivative corresponds to the curvature or concavity of the graph. The graph of a function with a positive second derivative is upwardly concave, while the graph of a function with a negative second derivative curves in the ...

  7. Differential calculus - Wikipedia

    en.wikipedia.org/wiki/Differential_calculus

    velocity is the derivative (with respect to time) of an object's displacement (distance from the original position) acceleration is the derivative (with respect to time) of an object's velocity, that is, the second derivative (with respect to time) of an object's position. For example, if an object's position on a line is given by

  8. Related rates - Wikipedia

    en.wikipedia.org/wiki/Related_rates

    Differentiation with respect to time or one of the other variables requires application of the chain rule, [1] since most problems involve several variables. Fundamentally, if a function F {\displaystyle F} is defined such that F = f ( x ) {\displaystyle F=f(x)} , then the derivative of the function F {\displaystyle F} can be taken with respect ...

  9. Four-gradient - Wikipedia

    en.wikipedia.org/wiki/Four-gradient

    In this article, we place a negative sign on the spatial coordinates (the time-positive metric convention = ⁡ [,,,]). The factor of (1/ c ) is to keep the correct unit dimensionality , [length] −1 , for all components of the 4-vector and the (−1) is to keep the 4-gradient Lorentz covariant .

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