When studying kinematics (the study of motion) it is important to know a few essential mathematical equations. These equations can be further developed by the use of variable substitution, as well as other mathematical operations. When taking advanced physics courses, calculus is a recommended tool for making physics work easier, because it allows for the use of derivatives and integrals, which allow change to be measured much easier that other methods currently available.
The basic physics equations are based off of three units of measurement: mass, distance, and time. These are respectively identified as m (measured in kilograms), d (measured in meters) and t (measured in seconds).
The first basic kinematics equation is the velocity formula. This is very recognizable as the units do not really change when you view a velocity measurement. By looking at the very definition of velocity, (also known as speed, if there is no direction included with the magnitude) we can create a formula for calculating it.
The formula for velocity is the distance traveled by an object divided by the time it took to travel. Mathematically, it is written as v (in meters / second) = d (in meters) / t (in seconds).
The above formula assumes that the object in question is moving at a constant velocity. However, this is not always the case, and many times an object may move faster or slower as time passes. This is known as the concept of acceleration, and it is measured in meters divided by seconds divided by seconds. Logically, it is the measure of how fast the object speeds up (or slows down) as time passes. An easy example to see of this is when an object is falling through the air. In fact, scientists have measure the acceleration of an object due to the Earth’s gravity to be around 9.81 meters / second squared. Mathematically, the equation can be written mathematically as: a (acceleration measured in meters per second squared) = ( vf (final velocity of an object) – vi (initial velocity of an object)) / time.
These are simply the basics, and depending on the data provided, you can rearrange these formulae to suit the task at hand.
For example, the below formula can be used to calculate distance. Although it is much more complex, it uses a different set of data to calculate the same result. Mathematically, you can use the following equation: distance = (initial velocity * time) + (0.5 * acceleration * time squared).
If you are given either the initial velocity or final velocity of an object, but not the other, you can use the following formula to find the unknown value: final velocity = square root (initial velocity squared + 2 * acceleration * distance).
These formulae may seem abstract in nature, but they can easily be explained through a technique known as unit (or dimensional) analysis. If you know the units of the value you want to find, you can create these formulae for yourself by making sure that all the units add up. By taking the known formula for a certain value, and replacing that value into another formula, you can create an entirely new formula. Then by simply making sure all the units properly cancel out or become equal to the units for your unknown value.
These are just the basics of kinematics and the math related to this are of physics. The techniques of unit analysis and variable replacement can be used in almost any mathematical discipline, and it is a handy tool for creating complex formulae that can take whatever data is at hand and turn it onto the results that you need.