The image above is indigenous Crash Course and I experienced the equation the velocity is Delta.

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What walk the line over acceleration represent?

\$egingroup\$ median value.... Although over there are various conventions, so the is just my interpretation \$endgroup\$
Usually, a bar over a symbol way its average. Also, one deserve to use the icons \$left\$ can be offered to represent the same thing.

Usually, this typical is a time average, the is

\$\$left = frac1t_1-t_0intlimits_t_0^t_1 s(t) extrmdt\$\$

where either \$t_0 ightarrow -infty\$ and also \$t_1 ightarrow +infty\$, or \$t_0\$ is the begin of the experiment and \$t_1\$ its end.

In your case, suspect the experiment starts in ~ \$t=0\$ and also lasts \$Delta t\$, that gives

\$\$left = frac1Delta tintlimits_0^Delta t a(t) extrmdt = frac1Delta t intlimits_0^Delta t frac extrmdv extrmdt extrmdt = fracv(Delta t) - v(0)Delta t = fracDelta vDelta t\$\$

Notice the use of the prize \$Delta\$ to denote a variation of a function. Below for example \$Delta v\$ method the sports of the role \$v\$ of change \$t\$. Girlfriend could likewise encounter the prize \$ extrmdv\$: both \$Delta\$ and \$ extrmd\$ typical the same thing (ie.

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a sports of something), but \$ extrmd\$ means that the is one infinitesimal variation. Native a mathematical point of view, this is complete nonsense: what is a difference between a big, a normal, and a small variation ? and what perform big, small typical ? In fact, the distinction is that \$ extrmd\$ indicates implicitly a limit, if \$Delta\$ is simply a typical quantity. Climate whenever you view a \$ extrmds\$ rather of a \$Delta s\$, you should interpret it as when the sport of \$s\$ tend toward zero, climate ... You can now understand the notation \$frac extrmd extrmdt\$ to signify the temporal derivative. Let"s think about a role \$f(t)\$, then

\$\$f"(t) = lim_ extrmdt o 0 fracf(t+ extrmdt) - f(t) extrmdt = frac extrmdf extrmdt\$\$

Similarly, as soon as you room referring to a little quantity the something, and not a sports of something, you need to use the symbol \$delta\$ (which indicates a limit) and no symbol at all when the amount isn"t small. For example, if you take into consideration the warmth transferred during a totality experience, girlfriend could speak to it \$Q\$, while throughout a infinitesimal transformation it should be \$delta Q\$