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

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What walk the line above acceleration represent?  \$egingroup\$ mean value.... Although there are different conventions, so the is just my translate \$endgroup\$
The bar over the \$"a"\$ method average acceleration. It"s no a typo in the video. A bar above \$"v"\$ would denote average velocity.

A bar above any quantity suggests that it is the mean value of that quantity. Usually, a bar over a symbol method its average. Also, one have the right to use the icons \$left\$ can be used to denote the very 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 \$t_1 ightarrow +infty\$, or \$t_0\$ is the start of the experiment and \$t_1\$ that is end.

In your case, suspect the experiment starts in ~ \$t=0\$ and also lasts \$Delta t\$, it 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 usage of the symbol \$Delta\$ to represent a sport of a function. Here for instance \$Delta v\$ method the variation of the role \$v\$ of change \$t\$. Girlfriend could additionally encounter the price \$ extrmdv\$: both \$Delta\$ and also \$ extrmd\$ median the same thing (ie.

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a variation of something), however \$ extrmd\$ way that the is an infinitesimal variation. From a mathematical suggest of view, this is finish nonsense: what is a difference in between a big, a normal, and a small sport ? and what perform big, small median ? In fact, the difference is that \$ extrmd\$ suggests implicitly a limit, while \$Delta\$ is simply a common quantity. Then whenever you see a \$ extrmds\$ instead of a \$Delta s\$, friend should interpret it as when the variation of \$s\$ have tendency toward zero, climate ... You deserve to now recognize the notation \$frac extrmd extrmdt\$ to signify the temporal derivative. Let"s consider a role \$f(t)\$, then

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

Similarly, once you are referring to a small quantity the something, and not a variation of something, you should use the symbol \$delta\$ (which implies a limit) and also no symbol at all when the quantity isn"t small. For example, if you take into consideration the warmth transferred throughout a totality experience, friend could call it \$Q\$, while throughout a infinitesimal change it must be \$delta Q\$