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Newton’s first law states that $\Delta v=0$ unless acted on by an external force, $F_{\mathrm{net}}\neq0$.

Can someone explain to me what the $\Delta v$ symbol means?

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    $\begingroup$ I downvoted the question and the answers because elementary research will provide an answer and I don't think it's useful to the site to answer such elementary questions. $\endgroup$ – ZeroTheHero Aug 17 at 21:29
  • $\begingroup$ See also physics.stackexchange.com/q/153791/25301 for other uses of $\Delta$ (and other symbols). $\endgroup$ – Kyle Kanos Aug 18 at 11:26
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The $\Delta$ symbol means change. So $\Delta v= v_{\mathrm{final}}-v_{\mathrm{initial}}$ which is the change in $v$. If $v$ gets bigger then $\Delta v$ is positive and if $v$ gets smaller then $\Delta v$ is negative. $\Delta v=0$ means that $v$ does not change.

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    $\begingroup$ Approved also for me. But change=variation is the same, is not true? $\endgroup$ – Sebastiano Aug 17 at 21:11
  • $\begingroup$ Also note - the direction of the delta is normally final value minus initial value. $\endgroup$ – David White Aug 17 at 21:31
  • $\begingroup$ @Sebastiano it depends on the context. In ordinary usage yes, change = variation. But in the calculus of variations the term “variation” has a precise technical meaning that is not as simple as the technical meaning of $\Delta$ $\endgroup$ – Dale Aug 17 at 22:43
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    $\begingroup$ @Dale Thank you very much for your details. $\endgroup$ – Sebastiano Aug 18 at 8:04
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The $\Delta$ is a mathematical symbol and does not have a unique meaning. In this context provided in the original post (just as in very many other situations), it stands for "finite variation" (of velocity), in the sense that, if $\Delta \vec{v} := \vec{v}_1 - \vec{v}_2$, then $|\Delta \vec{v}|$ is not extremely small with respect to either $|\vec{v}_1|$ or $|\vec{v}_2|$.

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The symbol $\Delta$ is the Greek uppercase letter “delta”. It has many common uses in math and phycisc; in your case the following:

The uppercase letter Δ can be used to denote:

  • Change of any changeable quantity, in mathematics and the sciences (more specifically, the difference operator[4][5]); for example, in:
    $\,\\{\displaystyle {y_{2}-y_{1} \over x_{2}-x_{1}}={\Delta y \over \Delta x},}$

    the average change of y per unit x (i.e. the change of y over the change of x). Delta is the initial letter of the Greek word διαφορά diaphorá, "difference". (The small Latin letter d is used in much the same way for the notation of derivatives and differentials, which also describe change.)

(From Wikipedia, the free encyclopedia, the article Delta (letter).)

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