How to Derive the Kinematic Equations of Motion *with Calculus*

The title is pretty self explanatory. Decided to test out my new camera and microphone by recording a little derivation video. Because I want to do theory, these are particularly fun to make, so let me know if there are any other equations you'd like to see derived! Most importantly, work this out for yourself to see all of the pieces come together.

[giankk]

"This isn't a history class"
Respect my friend

[laneellisor]

Honest one of the most helpful channels I've found! Keep up the awesome videos!

[igorcara]

Very well explained! It would be cool if you could derive the equations for circular motion too (I'm studying them on this semester and I'm having trouble on making sense of it D:)

[amandasmusic]

It’s interesting to see how one year of physics has aged you so much haha

[wiseacredave]

When you integrate over time, the limits should be t-initial to t-final to be consistent with having x-initial and x-final, etc. In other words t-initial is not always = 0. Your notation is okay as long as you denote t as delta t, but this obscures the fact that sometimes you need a t-initial different than zero.

[liender]

I remember watching this video before taking any physics classes- now I’m a year and a lot of math classes through and I’m happy these equations don’t confuse me as much as they initially did 😅 I’m excited and yet extremely nervous for my future classes

[prithivikumar]

Dude I'm in eleventh grade n I had to derive all three for a midterm a few months ago and totally blanked out on the starting of the second equation. Then I remembered this. Thank you so much man😊😊

[hunterweber]

you're definitely my favorite channel. you should derive them from algebra next!

[nickwelker]

I just want to say thanks for your awesome physics videos, never stop uploading!!!

[OPAnaya]

I loved your video and clear and helpful explanation. I did not love that I kept reading your "a's" as curly "2's" . my problem, not yours. Thank you!

[tunapedia]

It would be very interesting to see a video about equations of linear elasticity. Stress strain relationship, Hooke's Law etc.. Full anisotropic versions would be icing on the cake :)

[edmund]

my professor today derived the final equation using algebra, so watching this video i was like "wtf andrew why you lie to me" but you are now forgiven my good sir

[AjinkyaMahajan]

Fabulous explanation. I wish my professors have taught me in this way

[prydt]

This was super helpful!!! I definitely agree that deriving equations is much better than just rote memorization!!

[FreeRoger]

0:36 mathematicians: kill me kill me kill me kill me

[mihirbose]

WOW. 🎉🎉 Yeahh this helped a LOT, thank you so much.

[Idk-hgjr]

Wait, at 1:12, how did you integrate int(dv) without a dt term at the back, is it allowed? And what does it mean to integrate without a dt term?

[NothingXMuch]

Thnx a bunch bro!! I've been struggling to derive the third equation!!! Good stuff!!

[nitinaravindraj]

I was struggling for two days trying to understand this concept. After finding this video, I know now how to derive the equations of motion using calculus.

[FernandoRodriguez-getg]

It's really cool that you made this video!