What does $\Delta$ stand for?

Question

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?

Answer 1

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.

Answer 2

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 $|\vec{v}_2|$.

Answer 3

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).)