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.
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".
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!
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?
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
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
No, it doesn't because imagine if you stopped for five seconds. The arc length of S(t) from 0 to 5 will be 5 but your total distance travelled from 0 to 5 will be 0
@@lukandrate9866 Average speed is equal to the distance travelled divided by the time taken to get there, it does not include the time you sit there waiting after you get there !.
On a final exam day during a summer course of mine. A student turned in the exam and then just headed back home without bringing his belongings (yes including his backpack)... I had to sit in the classroom to not only wait for the time to be up for the exam, but also...... for that guy to come back and pick up his things..... ps1. He was actually a decent student in the class. ps2. He admitted to me that he got back home already and realized he had forgotten his backpack....
I'm totally ok with this methodology. Velocity is a vector and Speed is a scalar. Average speed is the integral of the velocity function between t=0s and t=5s over the time interval, that is 4 m/s.. The average speed is a vector and I'm not sure how could be calculated..
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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.
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making the world a better place...
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".
I was having a huge trouble with my specialist maths and this video helps a lot😭💖
Now do it using vector calculus 😀💯
Also nice video I thought it was very intuitive
you enlightened me, sir. Thank you!
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!
Profesor de física, wowww.... me dio risa cuando te acercabas y luego retrocedías jajaja .... 🤣.... eres un heroico 💪💪💪
This is astonishing 😍😍😍😍😍😍😍😍😍😍😍it's my first time I feel that big difference between them
Interesting topic
Well .....I didn't consider the fact that it is all happening in one direction.....I assumed it to be following some wierd locus while travelling😏
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?
Cobalt314 only instantaneous speed is equal to the absolute value of instantaneous velocity
Cobalt314 Ya
Speed is a scalar... it is equal to ds/dt where ds/dt is the magnitude of the derivative of distance (arc length)
i was searching exact these questions explaniation.
thanks.
me too
at 3:00 Is it what we call as Lagrange's mean value theorem?
s(t)=t(t-3)^2, I just wanted to share this. : ) #YAY
Snejpu v(t)=t•2(t-3)+(t-3)^2 #Yay
Your house better be close as the v function will rapidly exceed light speed.
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
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.
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
No, it doesn't because imagine if you stopped for five seconds. The arc length of S(t) from 0 to 5 will be 5 but your total distance travelled from 0 to 5 will be 0
@@lukandrate9866 Average speed is equal to the distance travelled divided by the time taken to get there, it does not include the time you sit there waiting after you get there !.
@@ny6u uhmmmm yes
Lol no it actually does
You're best at both maths and physics.
At 0:45 why avg speed is |instantaneous velocity|? Shouldn't it be |average velocity|?
you saved me an A
Does anyone know that he has put Doraemon them song on background 😂
How did you derive a function of speed?
Thank you!
In Portuguese, both ''velocity'' and ''speed'' are translated as ''velocidade''
In spanish too
I'm confused. From your definition of velocity, if someone travels in a circle, their average velocity is 0 km/h. Is this correct?
Yes
It is vector quantity.Get a flashback into your mechanics or kinematics class.
Backpack? That's pretty forgetful
On a final exam day during a summer course of mine. A student turned in the exam and then just headed back home without bringing his belongings (yes including his backpack)...
I had to sit in the classroom to not only wait for the time to be up for the exam, but also...... for that guy to come back and pick up his things.....
ps1. He was actually a decent student in the class.
ps2. He admitted to me that he got back home already and realized he had forgotten his backpack....
blackpenredpen then average speed is 12m/s
I'm totally ok with this methodology. Velocity is a vector and Speed is a scalar.
Average speed is the integral of the velocity function between t=0s and t=5s over the time interval, that is 4 m/s..
The average speed is a vector and I'm not sure how could be calculated..
What happen if S(3) not equal to 0 ? (from the video)
i love you
V: integral(velocity)dt /t
S: integral(||velocity||)dt /t
Works in any number of dimensions, right? ||x||=e^real(ln(x))
Well, how can you make an equation from you walking? I've wonder this since school
keep tracks of time and position. then write an equation based on that. I have an example will work it out for this maybe this weekend or so.
OMG you reply!!!!! Christmas is coming early 😍😍😍 thank you sir
Glad to see that you are happy!
blackpenredpen i can't wait, i've been wondering about that as well
Bamboozled long story short. You keep track of your position and time, then write an equation for it.
How make sense t power 3 for speed
Do the calc 2 way #YAY
Nice revision , solved it in 45 seconds #YAY
😨 thumbnail formula does not match with the formula xd
Do some IMO, pls
First