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

You are watching: S with a line over it

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.See more: How Many Squares Are In This 2×2 Grid ? How Many Squares In A 2 X 2 Grid* 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 $delta Q$