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

[@gian2kk]

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

[@GauravThakur-hg3ic]

I have respect to history as a study and story based on human curiosity but I have no respect to history as a class subject!!!

[@amandasmusic628]

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

[@AndrewDotsonvideos]

Oh god hahaha

[@amandasmusic628]

Andrew Dotson Not necessarily a bad thing, the rugged look works for you haha

[@DavidPumpernickel]

And my god, how much 3 years has...

[@laneellisor7113]

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

[@AndrewDotsonvideos]

Chapman ellisor thanks so much!

[@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:)

[@AndrewDotsonvideos]

Igor Guilherme That's a good idea! Circular motion can definitely be tricky

[@baashaalbaashaal6427]

Igor Guilherme YESS DO THIS ONE PLEASE!

[@adambee9396]

Aren’t they the same? You just change position (x) to theta, velocity (v) to omega, and acceleration (a) for alpha. Deriving them should be the exact same.

[@nickwelker3075]

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

[@moazamkhan]

3:51 SHOTS FIRED

[@hunterweber7739]

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

[@AndrewDotsonvideos]

Hunter Weber I was thinking the same thing! I appreciate it!

[@sedeanimugamez5418]

Well that’s gay

[@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.

[@angelmendez-rivera351]

David Woodside No, that should not be a problem. The origin of a coordinate system x(t) vs t is completely arbitrary, so objectively speaking, there is never a reason to not let t(i) [initial time] be equal to 0. In fact, most professors encourage you to do this.

[@dhruvmk3055]

Nah. As long as x=x initial at t=0, you're fine.

[@0liender]

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

[@prithivikumar2919]

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😊😊

[@pabloastoreca8726]

very useful and understandable!

[@AndrewDotsonvideos]

Pablo pastorea thanks for the positive feedback !

[@mihirbose1532]

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

[@edmund3504]

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

[@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 :)

[@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!

[@AjinkyaMahajan]

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

[@Himawari_.]

still helping after 7 years. tq so much❤❤

[@Idk-hg8jr]

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?

[@FernandoRodriguez-ge2tg]

It's really cool that you made this video!

[@AndrewDotsonvideos]

Thank you!

[@xenomni1673]

How can you substitute v as vf? at 2:43 velocity is a function, but vf is a number

[@AshishSingh-753]

Vf is a limit

[@NothingXMuch101]

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

[@nitinaravindraj6753]

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.

[@prydt]

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

[@paulfitzerald4408]

Straight to the point! Quality video, bravo!

[@BeautyByJuliette14]

pls do more videos like this!! love these

[@milansvetec3814]

Dear Andrew, your videos are very informative and useful, but here you forgot to mention that in your calculations the acceleration a is a constant. In general acceleration could be time-dependent. If so you would have to know the time dependence a(t) before performing the integration.

[@ayanroy6888]

Sir it seems that you are a physics teacher.sir please give your WhatsApp no if my doubt clear with you.

[@angelmendez-rivera351]

It's implied that the accelaration is constant. This video is aimed at physics students, not math students.

[@PanioGuitarCovers]

How did you choose the limits for the integrals and how would they have changed if you had chosen other parameters?

[@angelmendez-rivera351]

Robert Dewan x-final and x-initial simply stand for arbitrary limits of integration labeled by x to signify that they have units of position. t and 0 correspond to this because there is no reason for the lower bound not to be 0. t is, once again, arbitrary. It is the free parameter, after all. So, there is no choosing the bounds of integration here. They are all arbitrary.

[@jacob_dmn]

AMAZING WAY OF EXPLAINING.. KEEP IT UP MAN

[@shaurya6573]

Differentiation of Sound Velocity (V) /Sound Frequency (F)

[@goncalofreitas2094]

Very good explanation! I love these videos with equations!

[@FrogsForBreakfast]

You've been a big help! Thanks!

[@danielavalos4950]

Why would you derive the change in velocity into final velocity

[@angelmendez-rivera351]

Daniel Avalos Because finding the final velocity is more useful in most contexts.

[@sancithajayakumar1360]

3:22 where does that 1/2 come from?.....can you please explain

[@adityasrivastava2925]

Because integral of at with respect to t is at^2 upon 2 so we can write it as 1/2 at^2

[@bigghost.5418]

Thank you so much sir ❤ love from India 🇮🇳

[@FreeRoger]

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

[@dioutoroo]

Hi! At 6:44, Could you explain about the integration so you get 1/2*Vf2-Vi2? Thank you🙏

[@broodje8607]

He first integrated v with respect to v so you get v^2 devided by 2 because of the reverse power rule and the he has to put in the limits of integration so you get (vf^2 - vi^2)1/2 this is the same as vf2/2 - vi2/2

[@nitinsharma7216]

I am a class 11th student and I got understood very well.

[@simplistic6239]

"This isn't a history lesson" lmao

[@nocturno5373]

Just watching calculus for fun this was great! thanks

[@olusanyadeborah2893]

Finally seen an English version

[@SoloBSD]

I loved this one! Excellent!

[@MrMas9]

What about x=(t*(vi + vf))/2

[@marcioamaral7511]

Use geometry

[@marcioamaral7511]

secretly a trapezoid

[@farzadsidhva9995]

Very well explained !!

[@changenoways9555]

For the first equation of motion ,why did you choose your limits for adt as 0 and t but for dv you chose vi and vf? why didnt you choose 0 for vi? conversly, why was 0 chosen for ai?

[@changenoways9555]

never mind you answered it later in the vid. You read my mind

[@gustavoespinoza7940]

How does this work near a rotating black hole at scales less near a Planck length Also I think your f = ma is wrong It’s suppose to be f = am

[@leilaboitez7024]

Thank you! This was so useful ♥️

[@20.rahuljain25]

so helpful buddy loved it thnxx

[@armandol1826]

Great video. Quick question. One of my friend thinks that he'll be able to receive a bachelor's degree in physics without a higher level of math. What course would you say is at the very least necessary?

[@AndrewDotsonvideos]

All physics majors at my university are required to at least go up to Multi-variable Calculus and Differential Equations, and then take a 300 level math elective of their choice (Mine was Linear Algebra). This leaves you only 2 math courses shy of a minor in math which is why a lot of physics majors do that as well ( I took Real Analysis and Partial Differential Equations to get my minor). Hope this helps!

[@angelmendez-rivera351]

Hugo Lizardi I know this comment is late, but just so you know, it is virtually impossible to study physics without at least taking multivariable calculus and differential equations, both of which have linear algebra as a prerequisite. So, it is virtually impossible to study even mid-level physics without studying high-level maths.

[@mateosabando]

excellent video my friend!!!

[@dragonproductions9328]

Love it sir I just got it very nicely And i understood it Thank you sir

[@mathiyazhaganponmalai1244]

Thank you so much bro , from India

[@danielwright4987]

how do i make you my TA?

[@yasmeengabr]

sooooo sooo life saving .. THANK YOU

[@sanchits.4785]

Awesome Video.. Such a great explaination

[@armenpoghosyan4998]

Thanks for the help dad

[@kinshukmangal8940]

please derive the equation for the viscosity

[@joefuentes2977]

Yes the full one with the rank four tensor!

[@piccolaradge8333]

but HOW do you actually memorize these equations?

[@localboys7449]

Ms Eshiba-Emir Keep working with them and you’ll eventually write them without needing to derive them

[@angelmendez-rivera351]

You don't memorize equations. You learn them.

[@caperider1160]

Hi. You misused equal sign once along the line.

[@yatharthbakshi]

Try doing a voiceover of videos. The sound is kinda low.

[@AndrewDotsonvideos]

Thanks for letting me know!

[@yepitsme9341]

Thank you helped a lot

[@sineadsuter9188]

Very helpful!

[@thelastcube.]

I learnt that in school in the last year (I'm still in high school) but yeah this was a cool revision session, also do 'a day in the life of a physics major' part 2 😊

[@AndrewDotsonvideos]

Chaitanya Singh that's awesome! I'll definitely make more of those once classes start back up!

[@Deadly_Gaming7]

Love from India😇

[@JuiceBoxBoiii]

Thank you very much!

[@abelmedina-aispuro3716]

Bravo 👏🏻

[@safwanakhtar2528]

Hello im currently in secondary school(English high school) and i was hoping if you could guide me through physics, what should i start with?

[@QsHsNation1]

Halliday Resnick & Walker - Fundamentals of Physics (if you have a good grasp on calculus)

[@safwanakhtar2528]

QsHsNation1 how about any tv shows

[@QsHsNation1]

mmmm, carl sagans cosmos are a good place to learn some general stuff. but if you want to really learn physics, you will need to dig into the mathematics.

[@user-vq3lk]

Thank you

[@fanarts5290]

x=vft - (1/2)at^2

[@AndrewDotsonvideos]

depends how you define a

[@ManishKumar-bz3rg]

Bernaulli's theorem

[@bigm9676]

dope man!

[@denverchamberlain9657]

well done :)

[@AdamBehnam]

Awesome video, but poor sound quality! :/

[@joshnicholson6194]

God, looking at physicists do math is always weird, it is not wrong, but it is just not generally right. It is fun to look at it though, to think about why it is okay to break the rules in these contexts.

[@AndrewDotsonvideos]

What rules do you see being broken?

[@thomasmuntzer1004]

Well the first derivation is only true for constant acceleration

[@thomasmuntzer1004]

@Smit Shilpatul true dat, I do not know what the f i was thinking

[@levicaptain321]

"multiply bothsides by dt" that's not calculus..

[@raresr4282]

thx

[@Heezybeats1]

the third one was hardest

[@viradeus4322]

Yep calculus makes things a lot easier.

[@gabriopiola9246]

Umm there is a wrong = And some math passage a bit non mathematician Better was dv=a*dt--->v*dv=a*dt*dx/ dt----->v*dv=a *dx

[@noahkingston3151]

helpful

[@mikee-fl8ex]

*with basic Calculus*

[@mohannadislaieh3009]

Nice

[@sunisanthosh9711]

Okay ....im in 9th grade and iv3 no idea what those triangle thingies are 😐😑😑 can you make a a simple version of this video? Please?

[@AndrewDotsonvideos]

Suni Santhosh I do have a video of this with out calculus

[@adamharoon6021]

The "triangle thinges" are deltas which means change in. That isn't a calculus concept it is just algebra and is usually introduced with slope, something most people learn in algebra 1.

[@ahmetaltunoluk9486]

2:43 :))))))

[@mwizachali337]

wow

[@varghesekp8465]

nyssss.............

[@siamsama2983]

Woah

[@Heezybeats1]

bro, u write 'a' like 2

[@Pleasure_Baron]

if that's how you write two's, then you write like a kindergartner.

[@madamehydra1752]

Why he looks like Robert Pattinson for me...???