how to find the average velocity and the average speed? Calculus 1 tutorial

Learn the difference between the average velocity and the average speed of a moving particle. Remember the average velocity is always the change in distance divided by the change in time but the average speed is the total distance divided by the change in time.

#blackpenredpen #math #calculus

[historybuff]

The first part of the problem nicely illustrates the procedure for finding the average value of a function. Analytically, to find the average value of the velocity function, one integrates the velocity function to get the distance function and then plugs in the given limits of integration and then divides by the difference between these limits. This is equivalent to finding the ratio of the change of position to the change in time.

[younghanie]

I was having a huge trouble with my specialist maths and this video helps a lot😭💖

[WisdomVendor]

this is fairly easy. The hard part would be measuring the distance an object traveled and changed directions and measuring again distance and stopping and changed directions and recording the time involved all along and then writing a position function to represent that path followed. I don't think it can be done which is why I lend little merit to 'solving' a position function which is "given".

[aboveandbeyond.]

Now do it using vector calculus 😀💯

Also nice video I thought it was very intuitive <3

[soumyachandrakar]

at 3:00 Is it what we call as Lagrange's mean value theorem?

[bobacaxi]

You could have used the sign function, so you don't need to bother with grafics:
∫ |v(t)| dt = Speed
v(t)=d/dt(S(t)) and the upper bound you can set to be just "t" and the lower the initial time, or whatever you want.
|v(t)|=v(t)sgn(v(t))
∫ |v(t)| dt = S(t)*sgn(v(t))
But it was a great analysis and your videos are really awesome!

[comingshoon]

Profesor de física, wowww.... me dio risa cuando te acercabas y luego retrocedías jajaja .... 🤣.... eres un heroico 💪💪💪

[Humongastone]

At 0:45 why avg speed is |instantaneous velocity|? Shouldn't it be |average velocity|?

[math]

This is astonishing 😍😍😍😍😍😍😍😍😍😍😍it's my first time I feel that big difference between them

[vaishalipatel]

Does anyone know that he has put Doraemon them song on background 😂

[terrencereid]

very good job educating the youth. thankful for people like you.
making the world a better place...

[avinashkumar]

i was searching exact these questions explaniation.
thanks.

[cobalt]

So, is it true that speed would just be the absolute value of the velocity? Like, if you were to integrate velocity divided by the time interval to get average velocity, would you integrate average velocity divided by the time interval to get average speed?

[mutenfuyael]

Speed is the derivate of position, and the average of a function is the intagrate of this function divided by the difference of time, so I thought it was the intagrate from 0 to 5 of thé derivative of the position divided by 5 (so s(5)-s(0))/5, but I was wrong

[saiprasadhakki]

How did you derive a function of speed?

[snejpu]

s(t)=t(t-3)^2, I just wanted to share this. : ) #YAY

[JB-ymup]

Your house better be close as the v function will rapidly exceed light speed.

[japotillor]

For speed we use v as well, velocity usually is v with a vector arrow (physicist pet peeve :p). And yes seconds have symbol s. But otherwise perfect.

[nyu]

If s(t) describes the displacement of the particle then why wouldn’t the arc length of s(t) from t=0 to t=5 not describe the total length traveled ? thefore the average speed will be 29.07/5=5.814m/s

[Ray-obuq]

Well didn't consider the fact that it is all happening in one assumed it to be following some wierd locus while travelling😏