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 $delta Q$