# What does $\Delta$ stand for? [duplicate]

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?

• 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. – ZeroTheHero Aug 17 '19 at 21:29
• See also physics.stackexchange.com/q/153791/25301 for other uses of $\Delta$ (and other symbols). – Kyle Kanos Aug 18 '19 at 11:26

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.

• Approved also for me. But change=variation is the same, is not true? – Sebastiano Aug 17 '19 at 21:11
• Also note - the direction of the delta is normally final value minus initial value. – David White Aug 17 '19 at 21:31
• @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 $\Delta$ – Dale Aug 17 '19 at 22:43
• @Dale Thank you very much for your details. – Sebastiano Aug 18 '19 at 8:04

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 $$|\vec{v}_2|$$.

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.)