What is the meaning of $d$? Is is Delta? If it is Delta, why is it then not $\Delta$? I am still confused with that. Can someone help explain it to me?
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1See https://en.wikipedia.org/wiki/Total_derivative, or for more basic info https://en.wikipedia.org/wiki/Derivative – DomDoe Mar 07 '19 at 10:29
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4I asked a question about this a few years ago: https://physics.stackexchange.com/q/153791/ There is a good answer there with a detailed list of many such closely related symbols. Basically, $\mathrm d$ and $\Delta$ both mean a difference in a quantity. $\mathrm d$ just means an infinitely small difference. – Steeven Mar 07 '19 at 10:31
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3You need to take up differential calculus. – my2cts Mar 07 '19 at 10:44
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2In words $\frac{d}{dt}$ means "rate of change with respect to time". So in words Newton's Second Law is "force ($\vec F$) is the rate of change of momentum ($\vec p$) with respect to time". The equation is a more concise and more precise way of stating this. – gandalf61 Mar 07 '19 at 10:52
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While it's more on the mathematical side, this Wikipedia article should answer your question in more detail (or also here
For physicist, $d/dt$ is the time derivative of a quantity, $\vec{p}$ in your case. So what your formula says is that "force $\vec{F}$ is the time derivative (the change over time) of momentum $\vec{p}$".
This is somewhat related to Delta ($\Delta$). For linear functions, one can calculate the slope $s$ via "rise over run", $$ s = \frac{\Delta y}{\Delta x} $$ If your function is not linear, you can still approximate the slope for a short section with this. To get more accurate results, you can shorten your Delta. In the limit of $\Delta \to 0$, you get the differential mentioned in the Wiki article. Mathematically, the slope at point $x_0$ is then also called the derivative of $f$ at $x_0$ $$ s = f'(x_0) = \lim_{\Delta x \to 0} \frac{f(x_0+\Delta x) - f(x_0)}{\Delta x} $$ So, the force $\vec{F}$ is the time derivative of your momentum $\vec{p}$, $$ \vec{F}=\frac{d \vec{p}}{dt} = \frac{d}{dt} \vec{p} $$ EDIT: so, what the answer to the question "what is the meaning of $d$?" should probably be is: if you make your $\Delta$ really, really small (infinitesimally small, to be precise), you get $d$.
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Have you taken calculus before? $d \neq \Delta$, they don't mean the same thing as symbols. It's a limit from the discrete to the continuous. – cxx Mar 07 '19 at 16:20
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