Fluxion

Time derivative§

Newton at his time already knew what time derivative is, although he call it a "Fluxion". So, let us quickly glims through the calculus of physics, a time derivative put simply, is

$$\frac{\mathrm{d}f(t)}{\mathrm{d}t}:=\lim_{\Delta t \to 0}{\frac{\Delta f(t)}{\Delta t}} \quad \text{where } f(t) \text{ changes with respect to } t$$

$\Delta$ indicate a change of the value of anything, in this case, change of the value of the function $f$ and the change in time, when taken to the limit where $\Delta t \to 0$, we define this as the time derivative, notation are as shown above.

Displacement§

For a quick review, displacement is the distant measured in all basis combined, or so called a vector, thus, someone standing $3\mathrm{m}$ to the front then $4\mathrm{m}$ to the right from me have a displacement of

$$\vec s = (3,4) \qquad \text{or} \qquad \vec s = \begin{pmatrix}3 \\ 4\end{pmatrix}$$

Velocity§

This is average velocity

$$\frac{\Delta s(t)}{\Delta t}$$

This is instotanous velocity

$$\frac{\mathrm{d}s(t)}{\mathrm{d}t}$$