The Velocity Problem | Part I: Numerically

If I know my location at two different times, what is my velocity? There are two different notions to consider: average velocity - over an interval - and instantaneous velocity - at a point. This comparison will lead us to the idea of the limit, and in the future, the idea of the derivative, two of the foundational concepts in Calculus.

Learning Objectives:
1) Compute the average velocity over an interval
2) Describe the difference between average and instantaneous velocity

Now it's your turn:
1) Summarize the big idea of this video in your own words
2) Write down anything you are unsure about to think about later
3) What questions for the future do you have? Where are we going with this content?
4) Can you come up with your own sample test problem on this material? Solve it!

Learning mathematics is best done by actually DOING mathematics. A video like this can only ever be a starting point. I might show you the basic ideas, definitions, formulas, and examples, but to truly master calculus means that you have to spend time - a lot of time! - sitting down and trying problems yourself, asking questions, and thinking about mathematics. So before you go on to the next video, pause and go THINK.

This video is part of a Calculus course taught by Dr. Trefor Bazett at the University of Cincinnati.

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[mihirrao]

For anyone beginning their journey in Calculus, this is the man you want to trust. His explanations are to the point, intuitive and easy to understand (Let's hope he continues his amazing work covering things like Complex Analysis). Watch his videos, make rough notes, read the corresponding chapter from a proper calculus textbook (I personally felt that Calculus : Early Transcendentals by Howard Anton covers the material in a similar way/order as he has done in his courses ) and, finally, solve an appropriate number of problems to get the hang of it.

[somethingtojenga]

HUGE RESPECT for this guy being able to write every single thing backwards. I don't want any replies talking any nonsense about mirroring the footage--this man is left-handed and a perfect backwards writer and you will never convince me.

[rishavkumar]

Hello sir, i am an engineering student from india ... i want to thank you from the bottom of my heart for making these videos

[heykayhere]

Graduated college a long time ago and forgot all about Calculus. But it is quite fun to study again without any pressure from quizzes and tests. :)

[josheckertmedia]

I just wanted to thank u sir. I got through the entirety of my college calc 1 from my teacher just sending us your videos because she didn’t teach us at all😂. Your a true life saver

[jamieson]

I just want to say how personally grateful I am for your incredible videos. I'm in my late 30s and I've always wanted to go back and build and really understand the math that I had enjoyed when I was younger, but also struggled to understand concepts at times. These videos are made with incredible attention to detail, and it clearly shows in your work.

Thank you, thank you, thank you.

[nightowl]

Can we just take a moment and say how amazing it is that this man is teaching while writing everything backwards from his end. Amazing!!! Great videos, it's gonna help me so much during my Calculus I journey !!!!

[roshanasandadini]

Oh my goodness! What an explanation. I knew the definition of limit before, but I watched till the end because the explanation was superb. I really appreciate your work, and I have never heard of such an explanation like this. The way you explain is amazing in all of your videos. I am writing this comment to show my gratitude to you, sir.

[saityusufbulur]

Great explanation. To sum up, there's no such thing as instantaneous velocity. Expression "instantaneous velocity" is a simplified placeholder for "Average velocity measured between a specific moment and another moment a very tiny time before that moment". If the gap between two moments is tiny enough, you can ignore that gap and think of it as a single moment.

[daviddalton]

Thank you Dr Bazett, I would like to see more videos about Probability and Statistics as they relate to Data Science

[dinospumoni]

Are you writing forwards then flipping the video horizontally? That threw me for a loop for a second. Clever idea.

[Anne-gd]

Oh! Now I can understood the idea to calculate instantaneous velocity. If you're in a cop and wants to calculate the instantaneous velocity of the car before you then you have to send a beam of lesar towards it and after fraction of few seconds later you send another beam of laser. Thus by applying concept of average velocity over that small interval we're able to grasp instantaneous velocity as instantaneous velocity is a limiting process.

Thanks you sir for that spectacular explaining. ..☺☺

[mubashartariq]

Guy is blessed with amazing ability to teach

[robpatterson]

I am so happy I found your videos! They are truly going to help my extremely need for learning on a penny budget! I very much appreciate these videos!

[continnum_radhe-radhe]

I started this just for interest . Thank you sir for this amazing video.

[Kaizen]

Even though I learned all of Calculus already, I'm really excited to review and solidify what I've learned. Your lessons are great! Thanks for sharing them!

[KasunIshara]

I like the way you are teaching. Nowadays, I'm following your videos. Very clear and helpful . Good luck.

[munozali]

Thank you so much for all your videos, Dr. Trefor Bazett. I like your enthusiasm and your many examples. I use your videos in my classes often.

[jeanjulmis]

I know I have already taken Calculus I, but it's always fun learning a subject from different approaches.

[anushkagupta]

Your lectures are phenominal.loved the way of your teaching and animation.