Deriving Motion Equations with Drag Force

[@christopherlecompte1211]

I am literally teaching this today in 90 minutes! Perfect timing and thank you so much JTP!

[@FlippingPhysics]

Best of luck to you and your students!

[@iquityoutubeyoushouldtoo967]

u are a great teacher, very few know about you on youtube , how can i thank you ?? you are very very very great. trust me these are real words .

[@FlippingPhysics]

I list ways you can help out here: flippingphysics.com/help-out.html Thanks for the love!

[@beterax]

Probably the best video to truly understand what's going on.

[@o_sch]

I feel so proud of myself because I derived it by myself just now. I derived the position and velocity equations as a function of time from any acceleration all by myself when I taught myself derivatives. Then I tried to go onto drag but quickly got stuck in a loop trying to solve it like normal, as I did not know how to solve a differential equation. (I didn't even know what a differential equation was) I spent forever and ever to derive it but could not. I wanted to use it with the other motion equations in my code for physics stuff. I tried looking up position equations that factored in drag but none came up (as I now know is probably because if you take the derivative it would get quite long) I learned how to do differential equations today in an actual calculus class instead of my self teaching. I decided to finally conquer my goal of self deriving the equation. I started with a simple a = D(v) - g. Then dv/dt = a. I bundled all of the drag equation coefficients into k so D(v) = kv^2. Then I plugged in and simplified dv/dt = kv^2 - g and was left with g = kv^2 - v' This was a seperable first order so I used the property of it to separate it. Then I had to do an integral for that and this is the only time where i used the internet to find the common integral of 1/(-x^2 + 1) as 1/2(ln|x+1| - ln|x-1|). The rest of it was lots and lots of simplifying down to my answer: v = a(e^j + 1)/(e^j - 1), where j = -2ta/k and a = g/sqrt(gk) (a also is sqrt(kg)/k but I opted for the former because computers easily calculate inverse square roots) I graphed it in desmos and it does have asymptotes that are the terminal velocity, and changing parameters does realistically change it so I assume it is right. I still have to check with actual values.

[@eulersfollower7140]

Wow you never cease to amaze me with your teaching ,thank you for the wonderful content🎉🎉

[@FlippingPhysics]

Thanks for the love my friend!

[@darthTwin6]

Look's like I'll come back to this video after I finished Calculus BC. That was some incredible math right there!

[@FlippingPhysics]

Good idea!

[@adamharoon6021]

What textbook(s) do you recommend for AP Physics C: Mechanics along with AP Physics C: E&M? I'm looking to self study the course but I can't decide on what textbook and edition I should get. By the way, great video! Your content has greatly assisted my understanding of physics. I'll be recommending your videos for AP Physics 1 to both my teacher and my classmates. Thank you so much!

[@Uwek212]

5:24 I was wondering where did the absolute value symbol go?

[@borisbukalov9407]

I prefer to first find the antiderivative in terms of the original variable, v in this case, and then substitute the limits. Harder to make a careless mistake this way. That's what I preach to my students.

[@gravitasiproject45]

thankyou for ur explanation, sorry sir, can we to find b value? cause i did'nt find untill now

[@charlesfournierletourneau9369]

What happens if using a positive initial velocity and next step using an angle to determine distance travelled?

[@karthikeyanandagiri596]

man I was stressing over how I was gonna take drag into consideration for my school project, and now I see this, you guys are live savers, i just wanted to ask though, would this equation still like work if instead of gravity, I used another constant force that is applied in a given time period?

[@andrewjustin256]

Mr. P, what if I describe the down as negative. Won't it change the graphs? Also in my A level physics curriculum, sometimes, down is defined positive and negative in kinematics of free fall, drag force, projectile motion, etc. I feel like this will chmage the graphs! Please reply on your earliest convenience! Thank you

[@FlippingPhysics]

If you instead derive down as negative in here, all of the graphs will be flipped over the horizontal axis. That's the only change.

[@andrewjustin256]

@FlippingPhysics Thank you for the confirmation. Also Mr. P, in my A level Physics, sometimes the question doesn't state explicitly none whatsoever about the graph whether down is to be taken negatively or positively. It simply asks us to plot the graph. What must I do in this case?

[@FlippingPhysics]

Typically, if positive/negative directions are not identified, then convention is followed: up + / down - right + / left - Etc. I would simply stick to that, unless you really want to identify otherwise, in which case you need to state that specifically. Honestly, I very rarely identify down as positive.

[@andrewjustin256]

@@FlippingPhysics I will lay it on the line, but ever since I've seen your Mechanics playlist, I invariably follow the above convention and right hand rule with pulleys if exist so. It even feels quirky to use positive down. Thank you so much for your advice!

[@cemalgulcen6000]

I like your old method of writing on a whiteboard more sir, I understand it is easier to produce with green screen but it no longer feels like a classroom with four people in it

[@preethisatheesh1302]

Idk tho this is nice too

[@MrBeklager]

What if you have a dragforce with v^2

[@17puttab]

Good job. But what happened to the whiteboard?

[@FlippingPhysics]

I find this is more legible, easier to produce, and easier to understand.

[@17puttab]

@@FlippingPhysics Okay, got you. I'm just missed the whiteboard a bit. Thanks!

[@maxmiller8915]

so helpful thank you man

[@brady0340]

SCHRODINGER WAVE EQUATION DERIVATION PLEASE

[@physicslab5787]

Nice explination ❤️

[@FlippingPhysics]

Thank you 🙂

[@isaacong]

You know that you can use a calculator to do the messy integrals on the APC exam, right? In fact, doing the integrals with a calculator saves a lot of time.

[@FlippingPhysics]

It may save a lot of time and you may be able to use the calculator on the APC exams, however, the vast majority of the questions on the APC exams are devoid of numbers which makes the calculator useless and requires you actually know how to do the calculus.

[@anony4717]

Thank you

[@ayanchoudhary044]

Thank you Sir

[@FlippingPhysics]

Welcome!