Equations | Anthology of Ideas

This is just a basic equation list, explanations can be found elsewhere. For the most part derivations are done for you, but it is beneficial to understand how an equation goes from one form to another.

One dimensional Equations of motion (along a single vector direction)
Velocity as a function of time : $v_{xf} = v_{xi} + a_x t$
Position as a function of time: $x_f = x_i + v_{xi}t + \frac{1}{2} a_x t^2$
Velocity as a function of position: $v^2_{xf} = v^2_{xi} + 2a_x ( x_f – x_i)<br />$

Projectile Motion
Horizontal motion
Velocity along x: $v_{xi} = v_i cos(\theta)$
Position from position as a function of time: $x_f = v_i cos(\theta)t$
Max Horizontal dist: $R = v^2_i \frac{sin( 2 \theta_i)}{g}$

Vertical Motion
Velocity along y: $v_{yi} = v_i sin(\theta)$
Position: from position as a function of time $y_f = y_i + v_{yi}t – \frac{1}{2} g*t^2$
Maximum Height: $h_{max} = v^2_{i} \frac{sin(\theta_i)}{2g}$

Circular Motion
Radial Acc: $a_r = v^2_r = a cos( \theta)$
Tan.

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This is a reference list with notes of all SI and derived units in physics. The notes provide a brief explanation of some of the more confusing elements, but be warned that the full explanation could take many pages, and may be explained elsewhere on this website.

Physics has only 5 base units. (Plus the SI units Mole and Candela, but these are rarely used in Physics.)

Name	Abbreviation (Symbol)	Standard Unit	Notes
Name	Abbreviation (Symbol)	Standard Unit	Notes
Length	l, x (for distances)	Meter (m)	A meter is defined as the distance light travels in a vacumm in $\frac{1}{299 792 458}$ of a second (in physics it is customary to use metric measurements although the basic principles apply if you to use feet instead of meters)
Mass	m, M (when used with measurements in meters)	Kilogram (kg)	A kilogram is defined as the weight of a specific platinum-iridium cylinder
Time	t	Second (s)	Seconds are defined as 9,192,631,770 vibrations of radiation from a cesium atom
Temparature	T	Kelvin (K)	A degree kelvin is defined as $\frac{1}{273.16}$ of the distance between absolute 0 and the triple point of water
Electric Current	I	Ampere (A)	An ampere is the amount of charge (C) passing through a surface per second, and is defined as the current which produces a force of $2*10^{-7}$ newtons per meter of length between two infinitely long, perfectly straight and parallel conductors with an infinitely small cross section separated by one meter in a vacuum..

Each of these base units is defined on fundamental constants, and all other units are based on these five units. At times it useful to break longer equations down to their most basic units to determine if the equation makes sense. The most common combinations of these basic units are given their own symbols and names. These common units are as follows.

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Calculus Based Physics Formulas: Mechanics

Units in Physics (mechanical, electricity, magnetism, light and optics) including Si units.