How to Derive Equations of Motion - With and Without Calculus

Here's how to derive the 4 major kinematic equations (aka: equations of motion) that are used to describe the motion of particles in physics.

I show how to derive the both with and without calculus.

These equations are valid only if accleration is constant. Acceleration can be equal to zero, however it can't change.

If you have a changing acceleration, then calculus must be used to get a different set of equations.

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[rampriya darshini]

thanks a million.

[AlexPleaseHelpDotCom]

You're welcome too!

[Swetlana0]

Thanks alot!

[AlexPleaseHelpDotCom]

You're welcome. :)

[AlexPleaseHelpDotCom]

You're welcome!

[Mjhond]

Steady I Really Like This Video How to Derive Equations of Motion With and Without Calculus

[DYoung2112]

Great video and nice explanations.THX

[Akfloatable]

I don't get How you derived the last equation!!! How do you know which equations to sub in and what not??? Someone help please!

[lazygamerz]

Have you done a video on how to rewrite and turn around equations to use them for other things? (To make really simple example, Ohms law is voltage divided by resistance equals ampere, so you can turn it around very easily and do ampere multiplied by resistance to get voltage and voltage divided by amperes to get resistance, how is this done in derivation, integration etc?) I'm not looking for the simple formulae, but the logic behind how one can change formulas (my teachers werent good at this)

[Nihar Srivastav]

thank you so so so much for this video!

[thejuice152003]

Is there any way to derive the last equation with calculus that you did with algebra?

I mean the one that you didn't cover with calculus but did cover with algebra. It's x-xi = 1/2(v + vi)t

My physics instructor told us to derive this formula with calculus but I don't see how. I think it's only based on average velocity, since acceleration will be constant.

[tokyowanderer009]

Omfg. The cure to my procrastination. I owe you an A in my Applied Physics class.

Cheers.

[Yourheartjustglows]

no, just simplifying delta(x)=vi(v-vi/a)+1/2*a*(v-v­i/a)^2. I figured out the other way, rather than t=(v-vi)/2 i used t=(x-xi)(2/v+vi)

[andy4tek]

x-xi = delta(x) if that's what you're not understanding

[Yourheartjustglows]

How do you simplify that equation right before getting the final "time independent equation" ? Or perhaps, what work is shown to get there?

[jenny julie]

i l0ve physics now,...i hope you were my schl teacher