How to use calculus in Kinematics - Displacement, Velocity & Acceleration

A tutorial on how to use differentiation and integration to find displacement, velocity and acceleration
This was requested via twitter @mathormaths

[@PointlessCirclePro]

I just became a first year mechanical engineer. When my teacher said we should have learned integration in high school and then just decided not to explain it for those who didn't know it, I nearly had a heart attack. I'm sitting in the computer lab now and everything makes perfect sense. Thank you so much, you are a life saver.

[@ninaaax5805]

How’s mechanical engineering?

[@davidbromfieldjr.234]

Uhm so are you gonna tell us how life is as an engineer ?

[@randomsomeguy156]

I'm guessing it's very time consuming

[@mrrealnobody4382]

Is he still alive

[@mdaburaihansk]

If u still alive yt!
Plz reply 😌

[@mukompashi775]

It's crazy how you are able to get things so clear in the last min before exam

[@beoptimistic5853]

th-cam.com/video/XPCgGT9BlrQ/w-d-xo.html 💐👍

[@istian_park]

then forget it after the exam

[@Natashatrisha]

😂😂😂

[@GingerMathematician]

Well structured connection between calculus and displacement, velocity and acceleration, thank you!

[@beoptimistic5853]

th-cam.com/video/XPCgGT9BlrQ/w-d-xo.html 💐👍

[@AliAisaBellend]

Thanks man, need it for IB higher maths

[@unknown-mn9wo]

After watching several videos I finally understood the connection between displacement/velocity and acceleration !! thank you

[@storminmormin14]

I’m a second year calculus student and was having the hardest time understanding how exactly to apply integration to my physics problems and just had the biggest “duh” moment ever at the 1 minute mark.

[@beoptimistic5853]

th-cam.com/video/fRyUf-GY754/w-d-xo.html

[@aadityavilassharma1802]

and here's me in class 11th (in india) which have 0 experience in calculus but still manage to understand this lecture

[@mdaburaihansk]

@@aadityavilassharma1802 calculus mein research karti hue &any calculus problem puchh sakte ho....

[@Mateo2000G]

YOU HAVE SAVED MY LIFE :D test in 3 days

[@goodvibes-relaxationchanne8903]

This has helped me alot! Thank you so much!!

[@thesoul3461]

need more like this. It waa so useful!

[@beoptimistic5853]

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[@harshwardhanpatil8568]

Thank you sir.... I respect your efforts

[@shikharpathak8171]

I seriously getting so much trouble in this section but after watching this all my doubt solved

[@dhairyaagrawal6863]

thank you , nice and quick video with all important information 🔥

[@Skylerride313]

thank you makes physics so much easier :)

[@metasysta5755]

Thanks. Really helped me learn this for my exam next week. :/

[@jagdishkarelia3648]

x=(t^3/3)-(5t^2/2)+6t+1 then the value d^2x/dt^2 when dx/dt is zero.....

[@maralphayer501]

Prof you said from displacement to velocity it is differentiation but solving you did integration ? I am confused !!

[@swashnasharma8691]

Thank you I was able know the kinematics

[@lucianoazor7864]

very good explanation, thanks a lot

[@ashain1463]

Legend you are bro

[@agamya8949]

Thank u... It really helped me

[@3dge7]

Hello, I need some help, I understand the methods and everything you say but the question I have on my Math part of my Physics degree is troubling me. Question is v=5/4cos(3/4t-1/2) - displacement of object at time=0 is 2m. Need to find displacement of object in terms of time t. What do I do with the 'cos'? Does it become sin? Hope too hear back

[@DJSoundKick]

Thanksss Bro... helped me alot!! thanks again :)

[@harshithanabar1087]

i am very great full i found this video 😌💯🙏

[@RanBlakePiano]

Very helpful!

[@ishaankulkarni1396]

AWESOME!!!

[@zaheerkhan9012]

Brro it really helped me alott thank you sooo muchh

[@jagdishkarelia3648]

great great great video very much helping....

[@anushree4289]

Thanks for saving me for my neet 😭

[@Sajjxd]

Thank you so much!!!!

[@paramrajeshirke26]

Thanks for ur help!

[@Will.Luff1107]

thanks nigga

[@sivaneswaranmuniandy2427]

7.48 why there is D. Suppose to be one unknown C right

[@robustloki]

I know im late but the unknown D is for the j component of velocity. Basically if you have it in vector form , both components will have unknown constants so he names the unknown constant of j component as D.

[@ankithvijay2423]

It means a lot to me

[@irajoshuamanuel8980]

Thank you so much

[@rohanmehta2959]

in the challenger question, where does that dt come from? The one you multiplty the 2J with before integrating it?

[@Hemant-yj9rp]

you are integrating with respect to time. so you have to write dt.

[@ohmarmyint9422]

A particle travels along a straight line such that its acceleration at time t seconds =(6t+1)metre per sec.when t=2 the displacement =12m and when t=3,displacement=34m. finf displacement and velocity when t=4.Please help me.thanks

[@shashankmenon2824]

Ohmar Myint 2 seconds ur welcome

[@PahadiAangan]

x = 75m , v = 52.5m/s. integrate the velocity. there will be 2 variables c and d along with t. now put the value of displacement for 2 and 3 each. with the 2 equations solve for c and d. then putting the value of c and d in the equation of displacement with respact to time , put t = 4 and u should obtain displacement. with the value of c u can find v also at t=4.

[@sherryho3001]

Thanks for the help!:)

[@hardayasingh2654]

thanks broo..it helped me alot..

[@sripriyar3916]

Very helpful dude, thx!!! 🥰

[@beoptimistic5853]

th-cam.com/video/XPCgGT9BlrQ/w-d-xo.html 💐💐👍

[@Apricotsify]

Thanks!

[@AlikTheStoryteller]

thanks dude

[@MegaMrDidier]

Hi sir! Thanks for your tutorial... Can you help me for this question please
S = 9t^2 + 6t^3 - 2t^4
Find the total distance travelled by the particle from t=0 to t=4

[@sushgupta1613]

+Michael Didier you integrate the function, and using definite integrals you find the area under the graph, that should give you the distance

[@MegaMrDidier]

+Sushane Vivek Gupta thank you!!!

[@sushgupta1613]

Sure. The integrating of that function is, 3t^3 + 1.5t^4 - (2/5)t^5. So, replace the values of t, and you'll get two answers. Subtract the one you got from t=0, from the one you get from t=4, that'll give you the area under the graph, which is the distance

[@saranshsingh5773]

hi i dont think its the right time to orrect as this was 2 years ago but i dont see the need of integrating that as if u integrate displacemnt u dont get displacement and they are asking for distance travelled when equation for displacement is given so dont u just use that in a definite integral
please correct me if i am wrong

[@fairyfellermasterstroke]

​@@saranshsingh5773That's what I thought as well. Also, hello 5 years later

[@jirinsjimin56]

konichiwa sensei arigato

[@jameserrylcanillas5941]

thank you!!!

[@harshiniborigi]

Sir plz say me this ans
If velocity is 4m/s then velocity after 0.8sec?(g=10)plzzzzz

[@thejourney.9112]

Harshini Borigi to 12 m/sec

[@mdaburaihansk]

after 10 years! 😐🥱

[@abhirajkane]

thanks helped a lot

[@mrrealnobody4382]

This video is older than my little brother lmao

[@cr-wahmi7629]

thanks very much for the great video but do you have anything about other types of given information like instantaneous rest and passing through the point O

[@darrylros681]

2:54 you keep on saying integrate instead of derivative and that gives a confusion to those who are new to the subject

[@beoptimistic5853]

th-cam.com/video/XPCgGT9BlrQ/w-d-xo.html 💐👍

[@McScubakis]

Good stuff thx

[@hamzahwaheed9528]

This is called variable acceleration

[@dominicringoma1520]

Thank yu vry much

[@beoptimistic5853]

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[@hishamhashim3603]

thank you

[@arunahardath4896]

THANK YOU VERY VERY VERYYY MUCH

[@beoptimistic5853]

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[@jyothirnishitha]

Thanku sir

[@flux-Crazi]

good vid 😃😃😃😃😃😃😃🥰🥰🥰🥰🥰🥰

[@ErolGelbul]

Did you just swear to us rigth away in the video?

[@CapitalProject01]

🙏🏼 ❤️

[@xxAKILLEESxx]

Way over my head....

[@Mo-bi1pk]

challenger* btw

[@beoptimistic5853]

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[@inno-03]

Excuse me, sir. I came to watch a math video; there was no reason to speak Asian. I'm already having a hard day and that did not help my situation. I've disliked your video because of your unprofessionalism. As a college student, I'd appreciate it if you did not waste my time. My exam is tomorrow and now, I had to waste more time writing this comment. Hope you change and this does not happen again. I'm considering reporting your channel cause if you think about it, its kind of racist.

[@Kublai_jesus]

s is never used for displacement. its always for distance. x is for displacement.

[@powerlvl15]

+Vatsalya Saini x is for position right?

[@Kublai_jesus]

yes. position is what is meant by displacement from a certain point.

[@tenton2000k]

You can use any symbol to represent any problem you are doing. You just need to be consistent with it in your calculations. The whole point of a symbol is to denote something after all.

[@janeemmanuel8885]

Vatsalya Saini i use g for displacement
THUG LIFE

[@j.kaimori3848]

The thing with TH-cam is it depends entirely on where you are for the notation, but usually the concept remains the same, working that out is a challenge but the videos are usually good anyway.