❖ Position, Velocity, Acceleration using Derivatives ❖

Understanding Position, Velocity, and Acceleration Functions
In this video, we dive into the fundamental concepts of position, velocity, and acceleration functions, exploring their relationships and how they are connected through calculus. You'll learn how velocity is the derivative of the position function, and acceleration is the derivative of velocity (or the second derivative of position). We'll walk through detailed examples to illustrate how these concepts work together in motion problems, providing both a mechanical process and a deeper theoretical understanding of these crucial mathematical ideas.
By the end of this video, you will learn:
How to find the velocity function from a given position function.
How to determine the acceleration as a derivative of velocity or the second derivative of position.
The intuitive relationships between position, velocity, and acceleration in real-world contexts.
If this video helps you out, don't forget to subscribe, comment, like, and share! Let your friends, teachers, or parents know about my videos, and spread the joy of learning math! :)
For more exclusive content and support, check out my Patreon:
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[@patrickjmt]

Hi all! Please post comments, questions and anything else on your mind in the comment section! Also, don’t forget to LIKE, THUMBS UP, and SUBSCRIBE! I’d appreciate it greatly :)

[@areejreaz410]

You got me through college, and now GRAD School. LOVE YOU!

[@ryanwalker4491]

I really miss your videos when it comes to my Physics class. You've gotten me through Algebra 2 all the way through Differential Equations, and I can't thank you enough. I'm lost when it comes to Physics

[@bolis925]

Studying 20 minutes before my Calc final :'( lol

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bruh 15 minutes till I am leaving for class to take a test

[@shamekarobinson8215]

Same

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Does this story have a happy ending? I need to know the results :(

[@gopro2027]

well, I dropped calc 2 a few weeks ago

[@venzeti]

same

[@LinnSpin]

I've learned more Calculus here than in my lectures, Thank you so much :)

[@johntyler7155]

Just cause you know 2 things doesn't mean you know calculus. Do you know fundamental theorem of calculus do you know how to calculate integrals when you cant use integration to solve an equation? You need to use approximation using Simpson's rule or trapezoids rule. Ect... I'm not trying to be mean.

[@bikewheeleater]

@@johntyler7155 i don't get why you said all that ,, they said they learned more here than their lectures like 5 years ago, not that they're now an all knowing calc genius or something lol

[@seungjunbaek1494]

@@johntyler7155 Do you not understand English??? She never said she knew everything about Calculus after watching this video. She literally just said that she learned more from this video than from her lectures...

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[@sneaky_2]

🙂

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I'm actually crying. This final will be the death of me

[@patrickjmt]

hopefully not!

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Famie Ann Are u alive? Btw, 2 days later, mine is final😭

[@bedirhanbaltas7759]

@@rfreakingd8992 So are you alive after 2 years? :)

[@rfreakingd8992]

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[@mrstealyorefrigerator2588]

@Dikshu Sharma simp

[@samanthahinton1091]

Your videos have increased my quality of life by leaps and bounds. Thank you.

[@danalowry500]

I've been teaching math for more than half a century and you have the gift! Good luck with your career.

[@patrickjmt]

thanks for the kind words and encouragement :) i'm slowly closing in on you in regards to length of time teaching :)

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@@patrickjmt God bless us both! 🙏

[@arnaud78]

PatrickJMT, your videos are fantastic. No-nonsense, clear and simple explanations. Keep up the good work!

[@brianwilliams949]

THANK YOU! Was just banging my head against a wall over a how derivatives relate to position, velocity, and acceleration. Knowing why it relates helps tremendously.

[@sneaky_2]

🙂

[@renan6827]

Thank you. You explained so well. I was really struggling to understand this concept of differentiate to get velocity and differentiate velocity to get acceleration. Now it all makes sense.

[@chriswass1176]

i have 4 weeks to save my calculus class! lets do this!

[@mateocsa]

Chris Wass how’d it go?

[@christinajacobe6151]

I have 8hours

[@Amanda-vh9rv]

Christina Jacobe omg how did you comment that right when I was about to type that I’m shook

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Amanda omg ... good luck!!!

[@williamzhou1795]

Chris Wass my math final is on Tuesday :(

[@krispypotato9524]

was this really the stuff i sat through totally blank in my class? thank you so much this video helped me a lot!!!

[@sneaky_2]

🙂

[@ameliagrossman2637]

Really helpful videos, thanks for doing them.

[@patrickjmt]

Absolutely my pleasure!

[@ravitejainapakurthi6854]

Hii

[@sneaky_2]

🙃🙂

[@christopherlambert7549]

Thank you for the videos. Some people are good at explaining things(you), and others are not..(current teacher).

[@3the4truth]

Dude, my car looks just like that AND I do have a hot date!!!! You're the man patrick

[@VegasStreetLights]

If you were not using your left hand I probably would not have watched this video, no matter how well you may have explained things. People need a break from monotony, singularity, what have you. Thank you for taking the time to help people learn. We do appreciate it, as your viewers!

[@stayflyxx]

Your videos are helping me a lot more than my prof. at times. SUBSCRIBED!

[@sneaky_2]

🙃🙂

[@handlexz]

"Maybe you got a hot date?" Nah brah, Ise doin Calc.

[@anonymoususer2271]

Lolol

[@gamingvibe1012]

Care on study

[@patrickjmt]

@juanpedro19840914 yes, i am sure it is. i am just saying you do not often see this idea discussed in a basic calculus class : )

[@EinPiannist]

Hi Patrick, thank you so much for all of your videos. They are literally saving me from failing my calculus class. It's so easy to understand the concepts from the way you explain them, unlike my professor over-complicates everything. You're awesome!

[@richmondm2960]

holy moly bro this helped me a lot for my engineering mechanics assignments and exams. i couldn't believe it that I passed the assignments and quizess. thank you so much.

[@imnotshrek870]

May I ask what is the conclusion of this problem?

[@AMKADID]

Simple, To the point, & Clear. Amazing explanation thank you Sir

[@wesaidsomething]

THANK YOU. I have a maths exam tomorrow and I could not recall for the life of me how to go from displacement to velocity to acceleration. What confused me was that in class we used x(t) not s(t). Thanks again!

[@نورالعين-ظ1ص]

could you please make another videos to explain the graph of derivative I have problem in graphing thanks a lot

[@alinaatasha5627]

Im 17 and getting ready for my exam. This really help thank you

[@gordonmiller7334]

Please show me how you got the original position function, S=5t3 +3t+8. And calculate position, velocity, and acceleration for my truck starting at rest and reaching 50 mph in 20 seconds. I will be most grateful.

[@faisalali2001]

Best video on this topic that I've seen so far. Many thanks!

[@dongsunlee5305]

you have been the best help when it comes to all of my cal exams and homework. cheers mate!!

[@ricchburglar]

An I the only one here that's learning calculus months before the exam.

[@Reivivus]

You use derivatives to calculate "slopes", "critical numbers (whether and where a graph rises and declines)", and inflection points (the point at which a graph switches concavity from a "U" (upper concavity) to an "upside down U) negative concavity" To find derivatives: (6x^2 +4x + 5)= 6(2)x^1= 12x (simply multiply the constant 6 by the power of 2 and subtract a power of one from that power) + (1)(4)...note: subtracting 1 from x^-1=0, so the power is discounted) + 0 because there is no x

[@lowkeyfuzZ]

Your videos are honestly very helpful :) Really makes me feel a scholar sometimes :D

[@jennydv]

I will forever be grateful for these videos. THANK YOU!

[@andream8671]

This guy explains this better than my teacher.

[@askashutosh8667]

Your video contribution are really productive and zeal boaster , motivators for the mass out here and there Thankyou ❤️ Wishing positivity keep up the great work 👍

[@lillycolens6725]

Damn u just saved meee......can't stop thanking you...

[@TodaySkate]

Patrick Never fails to clear a simple a problem, horribly explained a professor, thank you.

[@patrickjmt]

happy to help :)

[@TheRealFuzzyBunny]

The waxing on is the most useful part of this video. Thanks for doing it. I'm watching this now because I didn't remember what the relationship is between displacement, speed, and velocity was. I remembered the formulas and have no problem performing the math, but I don't remember why one is the derivative of the other. Continue to wax on, otherwise your students will be like me and only learn the mechanics and not understand when these formulas are useful. I'm an electrical engineering senior who struggles because I never understand when or why we're using derivatives. I have no problem with the math, but I never grasped the usage because I only learned the mechanics.

[@patrickjmt]

@juanpedro19840914 it is called ' jerk ' - you see this in physics and sometimes in a calculus class, but not so often

[@sage3803]

not me learning this for the first time 4 hours before my final in Calc.

[@vidhup6907]

How Did I find this aftr 10yrs

[@villain07__]

Just same as I did!!

[@pjsolinap4899]

Yes

[@vidhup6907]

@@pjsolinap4899☠️ i am three years older

[@bp56789]

Very helpful, we just started doing this in class. I knew how to do velocity (and asked the teacher questions to help conceptualize it), but on the test we have unprepared questions--and the teacher didn't go into acceleration.

[@elliptiic]

You wrote this comment 9 years ago, has learning calculus affected your life whatsoever? Because I would think that this is pointless and I very much dislike it.

[@aliyaismael7948]

this saved my life during my college days

[@samanthamm7344]

This was actually so helpful online school sucks 😤

[@mario0riam795]

thanks for the video bro, appreciate it .

[@lilyshamanova5941]

Thank you, God bless you!!!!

[@jennygan5429]

you saved my life thanks for that

[@21937jd]

me too

[@soup3544]

Thank you

[@nanotam89]

Most functions have a maximum amount of change of rate for instance the derivative of x^2 becomes zero at the third derivative and will continue to be so forever therefore the limit of F^n(x) of the function x^2 as n approaches infinity (and n represents the derivitives of f(x)) would be zero. If your question is say the lim of f^z(x)= x^n (where z is the derivative) as z and n both approach infinity I believe the answer would simply be (infinity)x. Think of derivative rules it makes sense.

[@Reivivus]

To find anti derivatives you simple add a 1 to the original power of x (or any variable raised to a power) and then divide by that new power...Thus, to find an anti-derivative you do the exact opposite as you would do with a derivative. You use this to find the area under a curve. There are more complex methods, too, because there are more complex equations. Thus the anti derivative of 6x^2 +4x +5= (6x^3)/3 + (4x^2)/2 + 5x and of 12x + 4 = 6x +4x ...which should seem familiar

[@paanezan2906]

thank you man, I used your video to help with my assignment.

[@ObeyBrandon]

add this to the calculus playlist!!

[@GuardianDiancie]

I'd rather watch you to learn Physics. Really understandable

[@patrickjmt]

come back any time

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Thank you so much!! You saved me from some overdue assignments.

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Thank u so much 😭❤️❤️❤️ U saved my life (and my GPA as well😂)

[@tomeveret5032]

The distance between the two bodies varies according to the formula s (t) = t ^ 4 + 3.t ^ 2 - 4, where t is time. Question: when will the distance between these bodies be zero? By solving the equation s (t) = 0, the numbers are: t1 = 1, t2 = -1, t3 = 2i, t4 = -2i, where i is a complex unit. Dear all, why do we accept solutions 1, -1 but discard solutions 2.i and -2.i ??

[@Enderbro3300]

This video started halfway through, I have no memory of watching it

[@shaban-ed9vx]

You are a great teacher 🤝

[@SKisgrahamgooch]

Well explained! this came up in my igcse maths paper!

That's a great car indeed! Excellent vid BTW!

[@danksink5108]

s = t^2 t = 1,2,3 s = 1,4,9 Find velocity at t = 3 s

[@smitagravat1063]

What is the meaning of that motion equation from where it came ? If u tell this i will make a problem comapre it to a normal problem and understand why it is hard to understand at first place...........

[@jaymunie236]

Thanks this really helps for my AP Calculus course

[@patrickjmt]

perfect, come back any time!

[@wackyguydude]

All of your videos have been very helpful. Thank you.

[@prashannagautam8971]

wow! thank you a hundreds for this brother!

[@sneaky_2]

🙂

[@Andres44342]

Thank you so much! I had never really understood this until I saw your video. Thank you so much! I appreciate it!

[@jeremyherron7494]

Patrick....you are a Math Beast!!

[@elliptiic]

thank you

[@rahulahuja3721]

Really great examples and explanation sir!

[@kulbirpanesar7374]

OMG, thank you so much!!

[@chronos3912]

Omg studying 15 mins before our finals in physics HUHUHU thank u

[@victoriad2377]

I really appreciate the end of the video!!

[@Supermario0727]

You always cheer me up. Thanks.

[@Giant97]

That was a great explanation and easy to understand. Thanks

[@Reivivus]

To find a derivative you have to reduce an equation. Today, I realized that the derivative of the Area of a circle is actually the Circumference of a circle. And if you can use the derivative to find the slope then you can find the tangent line By y-y1= f '(x)(x-x1) F' (x) indicates finding a derivative.

[@patrickjmt]

@AntiProtonBoy do not feed the trolls : ) that just encourages them

[@juanlynching3807]

thanks for the video, Patrick.

[@triple_tubers3314]

Have 10 hours before my calc test, HAHAHHAHA I'M NOT GONNA SLEEP

[@salmitchitumba8314]

Thanks for help on derivatives.

[@alshookryalsir4707]

Thanks for this gorgeous ❤️ explanation

[@michellek8957]

Hi Patrick :) Thanks for your helpful videos. I need to write the equation of the position s(t). For ex, a ball is propelled straight upward from ground with an initial velocity of 144 feet per second

[@Huzzzaifa]

Damn thats easy...I'm not even a math student, but I needed to learn this for my MCAT test. And this is the only video useful and easy

[@patrickjmt]

come back any time :)

[@11RIHAM]

thank you so much

[@zahsum]

Amazing video man

[@sajifazil4716]

Thank you bro...

[@frannylamasko5718]

that was a good explanation and some parts were funny too thanks my guy

[@timbo9396]

Nicely done. Thanks

[@elvispresley1196]

I would like to see a similar video like this one but cover the 3rd derivative.

[@SanjaySanjay-te5dl]

Thanks it helped me to do my assignment

[@BarniDeDino]

Absolute legend

[@hamadhalbahrani8781]

Great explanation Thank you very much

[@jazminekarunaratne709]

Love all of these videos!! They are super helpful!!!!

[@JavierBonillaC]

Thank you. I think it needs to be explained a little more intuitively. Why would such a “complicated” equation reveal the position of the particle. At least that needs some comment. I understand the procedure and can do it by memory after seeing once, but It doesn’t tell me much. I’m going to look for an example with a car or a rocket.

[@MrJay5939]

thanks a lot man, you saved my life

[@juraijbinjamal5313]

Thank you for making it so simple 😆😆😆😆💚

[@danieltesfay9121]

So helpful.Thank you very much indeed.

[@germanmartinez1994]

Thanks so much for this man! Super helpful, your channel is fantastic.

[@areebhisham6490]

THANK YOU VERY VERY MUCH!!! IT WAS A GREAT EXPLANATION.

[@sayantanchaudhuri4943]

Thanks a lot

[@sarahknoll7570]

I like how you stretched out the clip on your pen cap