N00b question about understanding what formulas are

[Niaboc67]

I am new to the world of Science & Mathematics but am eager to learn all I can. I go to my local library and open up books on the topic such as Physics, Engineering and Electronics and there are swathes of formulas all of which I don't understand. I stare at them wondering what keys they must hold, of which I am bewildered by. I try to understand but my mathematical understanding is up to only precalculus. What I want to know is if I have the general understanding of how formulas work down. Essentially in a formula you have some "variables" and some "numbers" and the variables are spots in which you can "fill-in" given data that you have. Like if you know what amount of electricity, physical force or weight of something you can just "plug-n-play" I know this is ultra simple way of putting it but this is my understanding so far. Are formulas essentially blueprints people painstakingly devised while using the information they gathered about the physical world around them and it's parameters and thus knowing them were able to gather up that data to form an "absolute proof" that would work for all possible combination of numbers/things thrown into the variable and chug out a specific and accurate result? and thus it becomes a plug-n-play. Am I on the right track here?

Thank you

 

[AdityaDev]

Formulas work very well in maths (like permutations and integration) and in chemistry. But i haven't used many formulas in physics. You can learn them but in certain situation like if acceleration is a function of time you can't use your kinematics equations. For this all you need to know Is basics. You just have to know dx/dt = v etc. When you know the basics and your strong in your concepts and when you have sufficient knowledge in calculus, formulas will play a lesser role. It's better to stay away from them if you don't understand the working. Read good books like Halliday resnick and solve problems from irodov to build your concepts.

 

[NascentOxygen]

Correctly applied, a formula can represent a concise summary of physical principles and relationships. Not only do we plug in data values, but we need the mathematical skills to re-arrange a formula to turn anyone of its variables into the subject of the formula.

It is also invaluable to be able to represent a formula as a graph to better demonstrate its dependency on a particular variable. These are skills you acquire only through practice, practice, and more practice.

 

[Niaboc67]

@NascentOxygen Ok, my thoughts were partially correct then? only that things must be re-arrange them when new things arise because it can be subject to change. And to make a graphical representation of the formula. I think I am understanding now.

@AdityaDev could you explain dx/dt = v? Is this the same as "rate of change" change in x over change in y equals v, velocity?

 

[SteamKing]

You can learn them but in certain situation like if acceleration is a function of time you can't use your kinematics equations.

This statement doesn't make any sense. Which kinematic equations can't you use if acceleration is a function of time? The general equations of kinematics were developed using time as the independent variable.

 

[AdityaDev]

@NascentOxygen Ok, my thoughts were partially correct then? only that things must be re-arrange them when new things arise because it can be subject to change. And to make a graphical representation of the formula. I think I am understanding now.

@AdityaDev could you explain dx/dt = v? Is this the same as "rate of change" change in x over change in y equals v, velocity?

dx means small change in displacement. dt means small change in time.hence dx/dt represents small change in displacement for the given small time interval.

 

[AdityaDev]

This statement doesn't make any sense. Which kinematic equations can't you use if acceleration is a function of time? The general equations of kinematics were developed using time as the independent variable.

Oh no... You can't use the kinematic equation: V=u+at, s=ut+0.5at^2 when acceleration is varying. This is a basic assumption. Eg. a(t)=t^2+c is the acceleration at any time t. Now if you apply s=ut+... You will obviously get wrong displacement. Hence we use dv/dt = a(t)... Integrate and find v(t).

 

[SteamKing]

That's why I specified 'general' equations. The constant acceleration kinematic equations are just one type.