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

Поделиться
HTML-код
  • Опубликовано: 2 янв 2025

Комментарии • 131

  • @gian2kk
    @gian2kk 6 лет назад +189

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

    • @GauravThakur-hg3ic
      @GauravThakur-hg3ic 3 года назад +2

      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
    @amandasmusic628 6 лет назад +207

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

  • @laneellisor7113
    @laneellisor7113 7 лет назад +48

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

  • @igorcara
    @igorcara 7 лет назад +97

    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
      @AndrewDotsonvideos  7 лет назад +30

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

    • @baashaalbaashaal6427
      @baashaalbaashaal6427 7 лет назад +6

      Igor Guilherme YESS DO THIS ONE PLEASE!

    • @adambee9396
      @adambee9396 5 лет назад +3

      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.

  • @hunterweber7739
    @hunterweber7739 7 лет назад +18

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

  • @nickwelker3075
    @nickwelker3075 4 года назад +2

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

  • @wiseacredave
    @wiseacredave 5 лет назад +35

    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
      @angelmendez-rivera351 5 лет назад +13

      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
      @dhruvmk3055 4 года назад +1

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

  • @pabloastoreca8726
    @pabloastoreca8726 7 лет назад +30

    very useful and understandable!

  • @edmund3504
    @edmund3504 5 лет назад +3

    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

  • @prithivikumar2919
    @prithivikumar2919 5 лет назад +4

    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😊😊

  • @0liender
    @0liender Год назад +1

    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

  • @AjinkyaMahajan
    @AjinkyaMahajan 5 лет назад +4

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

  • @moazamkhan
    @moazamkhan 11 месяцев назад +1

    3:51 SHOTS FIRED

  • @mihirbose1532
    @mihirbose1532 3 месяца назад +1

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

  • @FernandoRodriguez-ge2tg
    @FernandoRodriguez-ge2tg 7 лет назад +2

    It's really cool that you made this video!

  • @tunapedia
    @tunapedia 4 года назад +3

    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 :)

  • @xenomni1673
    @xenomni1673 4 года назад +1

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

  • @NothingXMuch101
    @NothingXMuch101 6 лет назад +2

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

  • @OPAnaya
    @OPAnaya 2 года назад +1

    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!

  • @prydt
    @prydt 4 года назад

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

  • @Idk-hg8jr
    @Idk-hg8jr Год назад

    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?

  • @Himawari_.
    @Himawari_. Месяц назад

    still helping after 7 years. tq so much❤❤

  • @paulfitzerald4408
    @paulfitzerald4408 3 года назад

    Straight to the point! Quality video, bravo!

  • @nitinaravindraj6753
    @nitinaravindraj6753 2 года назад

    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.

  • @sancithajayakumar1360
    @sancithajayakumar1360 3 года назад

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

    • @adityasrivastava2925
      @adityasrivastava2925 3 года назад

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

  • @dioutoroo
    @dioutoroo 4 года назад

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

    • @broodje8607
      @broodje8607 3 года назад +1

      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

  • @goncalofreitas2094
    @goncalofreitas2094 6 лет назад

    Very good explanation! I love these videos with equations!

  • @BeautyByJuliette14
    @BeautyByJuliette14 4 года назад +1

    pls do more videos like this!! love these

  • @PanioGuitarCovers
    @PanioGuitarCovers 5 лет назад +2

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

    • @angelmendez-rivera351
      @angelmendez-rivera351 5 лет назад

      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.

  • @bigghost.5418
    @bigghost.5418 6 месяцев назад

    Thank you so much sir ❤ love from India 🇮🇳

  • @jacob_dmn
    @jacob_dmn 3 года назад

    AMAZING WAY OF EXPLAINING.. KEEP IT UP MAN

  • @milansvetec3814
    @milansvetec3814 5 лет назад +1

    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
      @ayanroy6888 5 лет назад

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

    • @angelmendez-rivera351
      @angelmendez-rivera351 5 лет назад

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

  • @danielavalos4950
    @danielavalos4950 6 лет назад +3

    Why would you derive the change in velocity into final velocity

    • @angelmendez-rivera351
      @angelmendez-rivera351 5 лет назад

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

  • @mathiyazhaganponmalai1244
    @mathiyazhaganponmalai1244 6 лет назад +1

    Thank you so much bro , from India

  • @nocturno5373
    @nocturno5373 4 года назад

    Just watching calculus for fun this was great! thanks

  • @FrogsForBreakfast
    @FrogsForBreakfast 6 месяцев назад

    You've been a big help! Thanks!

  • @nitinsharma7216
    @nitinsharma7216 3 года назад +1

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

  • @sanchits.4785
    @sanchits.4785 6 лет назад

    Awesome Video.. Such a great explaination

  • @SoloBSD
    @SoloBSD 5 лет назад

    I loved this one! Excellent!

  • @dragonproductions9328
    @dragonproductions9328 4 года назад

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

  • @FreeRoger
    @FreeRoger 3 года назад +1

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

  • @leilaboitez7024
    @leilaboitez7024 3 года назад

    Thank you! This was so useful ♥️

  • @simplistic6239
    @simplistic6239 6 лет назад +5

    "This isn't a history lesson" lmao

  • @MrMas9
    @MrMas9 6 лет назад +5

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

  • @mateosabando
    @mateosabando 4 года назад

    excellent video my friend!!!

  • @20.rahuljain25
    @20.rahuljain25 3 года назад

    so helpful buddy loved it thnxx

  • @farzadsidhva9995
    @farzadsidhva9995 3 года назад

    Very well explained !!

  • @yasmeengabr
    @yasmeengabr 5 лет назад

    sooooo sooo life saving .. THANK YOU

  • @changenoways9555
    @changenoways9555 Год назад

    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
      @changenoways9555 Год назад

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

  • @olusanyadeborah2893
    @olusanyadeborah2893 2 года назад

    Finally seen an English version

  • @armandol1826
    @armandol1826 7 лет назад

    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
      @AndrewDotsonvideos  7 лет назад +3

      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
      @angelmendez-rivera351 5 лет назад

      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.

  • @Deadly_Gaming7
    @Deadly_Gaming7 Год назад

    Love from India😇

  • @danielwright4987
    @danielwright4987 3 года назад

    how do i make you my TA?

  • @piccolaradge8333
    @piccolaradge8333 6 лет назад +1

    but HOW do you actually memorize these equations?

    • @localboys7449
      @localboys7449 6 лет назад +1

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

    • @angelmendez-rivera351
      @angelmendez-rivera351 5 лет назад +1

      You don't memorize equations. You learn them.

  • @armenpoghosyan4998
    @armenpoghosyan4998 2 года назад

    Thanks for the help dad

  • @yatharthbakshi
    @yatharthbakshi 7 лет назад +1

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

  • @gustavoespinoza7940
    @gustavoespinoza7940 2 года назад

    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

  • @shaurya6573
    @shaurya6573 Год назад

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

  • @abelmedina-aispuro3716
    @abelmedina-aispuro3716 10 месяцев назад

    Bravo 👏🏻

  • @yepitsme9341
    @yepitsme9341 4 года назад

    Thank you helped a lot

  • @sineadsuter9188
    @sineadsuter9188 5 лет назад

    Very helpful!

  • @thelastcube.
    @thelastcube. 7 лет назад +1

    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
      @AndrewDotsonvideos  7 лет назад +2

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

  • @JuiceBoxBoiii
    @JuiceBoxBoiii 6 лет назад

    Thank you very much!

  • @kinshukmangal8940
    @kinshukmangal8940 5 лет назад +1

    please derive the equation for the viscosity

    • @joefuentes2977
      @joefuentes2977 3 года назад

      Yes the full one with the rank four tensor!

  • @caperider1160
    @caperider1160 5 лет назад

    Hi. You misused equal sign once along the line.

  • @bigm9676
    @bigm9676 5 лет назад

    dope man!

  • @user-vq3lk
    @user-vq3lk 2 года назад

    Thank you

  • @denverchamberlain9657
    @denverchamberlain9657 6 лет назад

    well done :)

  • @ManishKumar-bz3rg
    @ManishKumar-bz3rg 6 лет назад

    Bernaulli's theorem

  • @viradeus4322
    @viradeus4322 4 года назад

    Yep calculus makes things a lot easier.

  • @joshnicholson6194
    @joshnicholson6194 Год назад

    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.

  • @ahmetaltunoluk9486
    @ahmetaltunoluk9486 3 года назад +1

    2:43 :))))))

  • @raresr4282
    @raresr4282 4 года назад

    thx

  • @levicaptain321
    @levicaptain321 Год назад

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

  • @fanarts5290
    @fanarts5290 6 лет назад

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

  • @Heezybeats1
    @Heezybeats1 5 лет назад

    the third one was hardest

  • @noahkingston3151
    @noahkingston3151 5 лет назад

    helpful

  • @mohannadislaieh3009
    @mohannadislaieh3009 6 лет назад

    Nice

  • @safwanakhtar2528
    @safwanakhtar2528 6 лет назад +1

    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
      @QsHsNation1 6 лет назад

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

    • @safwanakhtar2528
      @safwanakhtar2528 6 лет назад

      QsHsNation1 how about any tv shows

    • @QsHsNation1
      @QsHsNation1 6 лет назад

      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.

  • @AdamBehnam
    @AdamBehnam 5 лет назад

    Awesome video, but poor sound quality! :/

  • @mikee-fl8ex
    @mikee-fl8ex 3 года назад

    *with basic Calculus*

  • @thomasmuntzer1004
    @thomasmuntzer1004 4 года назад

    Well the first derivation is only true for constant acceleration

    • @thomasmuntzer1004
      @thomasmuntzer1004 4 года назад

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

  • @gabriopiola9246
    @gabriopiola9246 4 года назад

    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

  • @varghesekp8465
    @varghesekp8465 7 лет назад

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

  • @mwizachali337
    @mwizachali337 5 лет назад

    wow

  • @siamsama2983
    @siamsama2983 6 лет назад

    Woah

  • @sunisanthosh9711
    @sunisanthosh9711 7 лет назад

    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
      @AndrewDotsonvideos  7 лет назад

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

    • @adamharoon6021
      @adamharoon6021 4 года назад

      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.

  • @Heezybeats1
    @Heezybeats1 5 лет назад

    bro, u write 'a' like 2

    • @Pleasure_Baron
      @Pleasure_Baron 5 лет назад

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

  • @madamehydra1752
    @madamehydra1752 2 года назад

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