Question

dervitation of time​

Answer 1

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Explanation:

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Answer 2

Answer:

A variety of notations are used to denote the time derivative. In addition to the normal (Leibniz's) notation,

{\displaystyle {\frac {dx}{dt}}}\frac {dx} {dt}

A very common short-hand notation used, especially in physics, is the 'over-dot'. I.E.

{\displaystyle {\dot {x}}}{\dot {x}}

(This is called Newton's notation)

Higher time derivatives are also used: the second derivative with respect to time is written as

{\displaystyle {\frac {d^{2}x}{dt^{2}}}}\frac {d^2x} {dt^2}

with the corresponding shorthand of {\displaystyle {\ddot {x}}}{\ddot {x}}.

As a generalization, the time derivative of a vector, say:

{\displaystyle {\vec {V}}=\left[v_{1},\ v_{2},\ v_{3},\cdots \right]\ ,} \vec V = \left[ v_1,\ v_2,\ v_3, \cdots \right] \ ,  

is defined as the vector whose components are the derivatives of the components of the original vector. That is,

{\displaystyle {\frac {d{\vec {V}}}{dt}}=\left[{\frac {dv_{1}}{dt}},{\frac {dv_{2}}{dt}},{\frac {dv_{3}}{dt}},\cdots \right]\ .} \frac {d \vec V } {dt} = \left[ \frac{ d v_1 }{dt},\frac {d  v_2 }{dt},\frac {d  v_3 }{dt}, \cdots \right] \ .

Explanation: