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A time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function. [1] The variable denoting time is usually written as t {\displaystyle t} .
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 = = =.
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
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 ...
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 ...
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 ...
Anyone watching the news following the presidential election has heard one word associated with President-elect Donald Trump more than any other: tariffs.
The covariant derivative incorporates the 4-gradient plus spacetime curvature effects via the Christoffel symbols The strong equivalence principle can be stated as: [ 4 ] : 184 "Any physical law which can be expressed in tensor notation in SR has exactly the same form in a locally inertial frame of a curved spacetime."