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So, the equations I'm talking about are the "big 4" listed here: https://www.physicsclassroom.com/class/1DKin/Lesson-6/Kinematic-Equations

I understand how to derive all these using calculus or algebra and graphs. That's not my problem. I can apply them pretty well to problems I need to solve as well.

I want to go a step further and understand *why* these equations work using my regular thinking processes, and not just kind of see how to step by step derive them. It's hard to explain what I mean.

For example, I *do* feel I "understand" the equation: vf=vi+a*t

The initial velocity is there because of inertia, and the acceleration is constant so knowing that and the time interval will give you how much the object has accelerated by. Thus, adding these, you get the final velocity. I feel I really *get* this equation and understand why it is true.

I do not feel the same way at all about the remaining three equations. Like I try to understand how these apply to an object moving at a constant acceleration, and I got nothin'. Can anyone help with this? Is it feasible to try and think like this as you go further in learning physics equations?

EDIT: Okay, I found a good explanation for the x=vi*t+.5*a*t^2 equation: https://www.physicsclassroom.com/class/1DKin/Lesson-6/Kinematic-Equations-and-Graphs

So I'm good with 2/4 of them now!

EDIT2: Okay, I got the one for average velocity times the time interval too now. Learned a bit working on that one, such as about what it means to average things (including the integral definition for the average value of a function over an interval). So, one more, I'll resume this tomorrow. Perhaps the more important remaining question is whether this sort of approach will work with more advanced topics? So, for example, the "understanding" of the displacement equations involved graphs. The understanding for the vf equation involved knowing about the law of inertia and just the definition of acceleration. A combination of working things out on my own and Googling.

I understand how to derive all these using calculus or algebra and graphs. That's not my problem. I can apply them pretty well to problems I need to solve as well.

I want to go a step further and understand *why* these equations work using my regular thinking processes, and not just kind of see how to step by step derive them. It's hard to explain what I mean.

For example, I *do* feel I "understand" the equation: vf=vi+a*t

The initial velocity is there because of inertia, and the acceleration is constant so knowing that and the time interval will give you how much the object has accelerated by. Thus, adding these, you get the final velocity. I feel I really *get* this equation and understand why it is true.

I do not feel the same way at all about the remaining three equations. Like I try to understand how these apply to an object moving at a constant acceleration, and I got nothin'. Can anyone help with this? Is it feasible to try and think like this as you go further in learning physics equations?

EDIT: Okay, I found a good explanation for the x=vi*t+.5*a*t^2 equation: https://www.physicsclassroom.com/class/1DKin/Lesson-6/Kinematic-Equations-and-Graphs

So I'm good with 2/4 of them now!

EDIT2: Okay, I got the one for average velocity times the time interval too now. Learned a bit working on that one, such as about what it means to average things (including the integral definition for the average value of a function over an interval). So, one more, I'll resume this tomorrow. Perhaps the more important remaining question is whether this sort of approach will work with more advanced topics? So, for example, the "understanding" of the displacement equations involved graphs. The understanding for the vf equation involved knowing about the law of inertia and just the definition of acceleration. A combination of working things out on my own and Googling.

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