When I get almost ran over by cars, I get scared, shocked, and I try to forget about it. When Vi gets almost ran over by one, she makes a youtube video carefully and mathematically explaining the situation to clear possible misconceptions surrounding the issue.
2 seconds later, you've still gone 20 metres and 2.1 seconds later you're still trying to ruin my day. What is this substance all over the ground? We don't know how to do math to it... Me when I almost get run over: Oh my god what is that lunatic doing? (3 seconds later) Oh my go- AAAAAA Vi: *Carefully explains exactly the derivatives in Calculus AB and draws graphs to explain the deceleration of the car*
What happens next? Usually, sadly, the driver gets out and yells at the pedestrian for being on the road. Why? There's a strong correllation between the sort of driver that doesn't pay attention to stopping for people on the road and the sort of driver who's generally a jerk to others.
It's been e^itau years since the last such video and tau over pi (as tau should be) years since she did this regularly. Not that I don't appreciate the other occasional videos, but this is why I subscribe to this channel. Excellent job as always.
This Padovan joke is as bad as the third and second last combined... This Pisot-Vijayaraghavan joke is always better than its Galois conjugate... etc. (I think we can all agree that all maths jokes are pretty horrid)
I never understood why you'd unsub if you want to see more content. If you stay subbed you might see more. If you unsub you definitely won't. Where is the logic?!
Sfs Aviation I’m not a fan of the furry community but calling someone disgusting and especially in all caps is terrible of you. Please keep in mind we’re all human.
I'll explain. The long pedal that makes the loud vroomy noises controls the second derivative of following distance, and is also the first derivative of crashing damage. It only operates in the positive direction. The fat wide pedal does very much the same, but only operates in the negative direction. The spinny thing you sit under controls the first derivative of theta. And if it rains really hard and you're going too fast, all of these things will start to act on their own derivative instead.
I seriously doubt that everyone needs to know calculus before being allowed to drive. Rather, they should just know to do A to achieve B. Let the scientists and mathematicians know the innards and complexities, while you tell more simple folk to break earlier and have fun. You don't need to know formulae and theory to practice it.
This was a really interesting video! I think another way to look at it could be from a physics perspective - when you brake on wet pavement vs. dry, the coefficient of friction is lower, so the force acting on your car to decelerate it would decrease. An interesting thing here is that if you slam on the brakes so that they skid, the force on the car would be kinetic friction instead of static, so it would actually take a longer time to stop than if you eased on the brakes making sure that the wheels don't slide along the road. Of course, finding out the exact coefficients of friction is impossible on a practical level and they vary between roads, and then when it boils down, the effects are pretty much the same as in your video. On the other hand, if you do know your car's rate of deceleration and its original speed, you can figure out exactly how far it will travel before stopping before you hit the brakes.
Arpit Bharti wat. I need to check this... I checked social blade, and this seems to be the first time she's reached 1 million. At least since 2012, when she only had 100k.
More drivers should take the time out of their day to watch this video! The math involved makes it easy to see how to be safer whilst driving in the rain. What I found the most fascinating was how slowing down won't necessarily make driving in the rain any safer. I was confused when they started breaking down the distance and speed using a line, but after watching it a second time, the illustration is more clear to me. This video inspired to think more mathematically about my driving. It caused me to also consider the effects of making more people think this way about driving in the rain and how it would make the roads a safer place.
The trick to driving in the rain is to shout ascending prime numbers into the clouds until you reach your destination. This way, the rain will understand that no matter how hard it tries, it'll never amount to what you are, and will leave you alone out of embarrassment.
Which brings to question, why do so many things covered in driver's ed use esitmated distance rather than time? It's usually easier to judge 4 seconds for the speed you're traveling than 150ft (or whatever). So it works well if you signal 4 seconds ahead, or give yourself 4 seconds of following space. Also when going on estimates for time, it automatically scales in proportion to the speed you're going.
In Canada we're taught to use no less than a 3-second following distance from other vehicles. That is, if the vehicle in front of you were to instantly stop and you were to keep driving at the same speed, you'd have 3 seconds before you collided with it. That gives you plenty of reaction time if, for example, the other vehicle slams on its brakes -- it also prevents the creation of phantom traffic jams caused by traffic waves. (youtube search: phantom traffic jam)
How is it that watching a Vi Hart herself video can make my day better? I don't know but I do care. Thanks for being here Vi. You are our treasure. Our - meaning the watchers, math fantasizers and those that listen to the fast but melodic voice that explains the math behind everything that interests her.
Angels? More like angles... Angles descending at an accelerating rate from the beautiful generative heavenly realm that can only be described as Vi Hart's mind.
I guess you were crossing on yellow, but basically everyone just has to leave a bit more space in front and also begin to brake earlier and exponentially
You know what we should do on Pi Day? Tau Hour. When's that? Six to eight (6 2 8), of course. But wait, that's two hours, isn't it? Well, that's kinda the point.
As someone who just took her license, it comes as a pleasant surprise that you just happened to pop up with the first video I have some form of previous knowledge about, regarding the subject you have chosen!
But what about Planck lengths, I'm watching this video at night with low volume so not sure if you already mentioned that but a Planck length is the shortest practical distance that you can go. So eventually you will come to an end of cutting roads in half.
The calculus we do while driving is subconscious. If it were conscious... traffic would flow at around max of 2MPH all the time. If 98% of the time, the roads are dry, you quickly learn the subconscious calculus to stop where you need to, no matter what speed you're going. But if a rare condition like rain or snow happens... you'll be in trouble if you're brain is driving on auto-pilot. This will probably also be a huge problem for self driving cars in the near future... even though they can do calculus "consciously" on the fly... because there are so many variables. The weight of the car, which affects it's momentum. The quality of the break pads. The tread on the tires. The roughness of the road surface, and the surface tension of the water on the road. All of that said... the worst drivers I've ever seen, by far, are taxi drivers.
Thanks for making me feel good about math again because I lost hope when I started my first college math in math theory (we call it foundations of mathematics) when all I could do was find derivatives and integrate stuff. Calculus has been bae.
Yay, another Vi video! Also yes, my high-school physics taught me so much more about what happens when I'm driving than the people who taught me to drive. Once you understand how momentum works, you really understand why 60kg me travelling at 1ms^-1 shouldn't mess with a 1t car travelling at 18ms^-1.
An interesting breakdown of the kind of stuff we do naturally within fractions of a second. Also: it's good to hear an explanation of how simply driving slower doesn't mean shit in wet conditions, it's all about the space you leave yourself and others and how you handle the vehicle. Reporting from Indiana and I can attest that rain destroys the already abysmal traffic flow around here. I think it's just a direct result of poor education in operation because it rains/snows here enough to where it shouldn't be a mystery for anybody.
Delighted to watch again a "classic Vihart":-) Looking forward to part 2, especially, should You tackle different options, to determin the slope, at a given point.
Much much bigger issue is when you are on sidewalks and not on crosswalks. Mainly because stopping or acceleration speed doesn't matter when you drive through a puddle in a high speed..
What I love most about Vihart is that she can talk about mathematics in such a romantic way by giving the concrete or asphalt example of calculus applied to driving. Math ceases to be a confusing abstract concept to me only until l have to do the math myself.
I really love Hermione Granger and want to be her. Mentioning this fact to my friend in passing, she told me I wasn't smart enough to to be her. My intelligence is really something I value, and I was super hurt, even though she was just being honest. Now I'm doubting my whole image of myself. Any advice?
I like that you applied math in a frequently occurring real life scenario. Some of the physics were confusing because I have yet to take a physics class. This inspires me to begin learning to drive because it gives me an idea as to how simple it can be. I like that it made a somewhat confusing driving scenario simple and understandable.
The physics of a car stopping is only part of it. Something not mentioned (and CGP Grey didn't mention in his last video) is that most of it is actually human reaction time. Yellow lights help, but at high distances (like some places where you drive over 50 with stoplights) it can be hard to discern if you're too close to stop in time (without completely slamming your brakes) or not. By the time some people process this, they're already too far to stop and are running a red light. Of course, some people just aren't paying attention, and that's the worst. I've been rear ended while stopped (it was red before I ever got to it) because someone behind me wasn't paying attention.
Acceleration is not change in speed over time but change in velocity over time. This makes really big difference if you think of circular motion of constant speeds - by your definition, the object in this motion experiences no acceleration what so ever. You could practically think of acceleration this way in motion along a line, but it is deceptive - if you think of acceleration of say 1 (m/s)/s, but you start with velocity of -1 m/s, then the chage in speed changes its behavior after the first second - from decreasing the speed to increasing it.
In this particular case, the direction of motion doesn't change so it's okay to use either speed or velocity. However, there are many situations where it would matter.
Somewhat off topic but this reminded me of my Real Analysis professor. He used to always say that cops should use the Mean Value Theorem (of derivatives) to catch people speeding xD
I've never thought about acceleration and deceleration like this before! While it is confusing, starts to make sense when you think about. I like how the graph showed different conditions and how the conditions affect acceleration and deceleration.
When I get almost ran over by cars, I get scared, shocked, and I try to forget about it.
When Vi gets almost ran over by one, she makes a youtube video carefully and mathematically explaining the situation to clear possible misconceptions surrounding the issue.
My Goodness! I was 1 foot away from being turned into a pancake by your bad math education.
made my day
You're here and then you're there and no one can explain this!
2 seconds later, you've still gone 20 metres and 2.1 seconds later you're still trying to ruin my day.
What is this substance all over the ground? We don't know how to do math to it...
Me when I almost get run over: Oh my god what is that lunatic doing? (3 seconds later) Oh my go- AAAAAA
Vi: *Carefully explains exactly the derivatives in Calculus AB and draws graphs to explain the deceleration of the car*
What happens next? Usually, sadly, the driver gets out and yells at the pedestrian for being on the road. Why? There's a strong correllation between the sort of driver that doesn't pay attention to stopping for people on the road and the sort of driver who's generally a jerk to others.
A.. a Vihart video... about math... not on Pi day... WITH A PART ONE POINT NINE REPEATING?!?! IS THIS MATH HEAVEN?
1.99999... = 2
This video is part 0.99999...
They said WITH a part 1.99999..., not that it IS one, but I can understand your confusion.
yessss
It's been e^itau years since the last such video and tau over pi (as tau should be) years since she did this regularly. Not that I don't appreciate the other occasional videos, but this is why I subscribe to this channel. Excellent job as always.
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I knew you were an anthropomorphic triangle all along
do not doubt the holy "tri" "angle"
*Viangle
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+
+
This fibonacci joke is as bad as the last two you heard combined...
Ha!
you've ben waiting to use that one, huh?
Why did the boy wear glasses in math class? To get better with "di"vision
I am writing this down.
This Padovan joke is as bad as the third and second last combined...
This Pisot-Vijayaraghavan joke is always better than its Galois conjugate...
etc.
(I think we can all agree that all maths jokes are pretty horrid)
It's always a little holiday when vhart uploads
+
True
Yep
ya. XD the best of holidays
And when she promises a part 2
Yay!!! I was waiting for you to post! no preasure!
ha same
And she left us with a cliffhanger. Surprising. Elegant.
lol same
same
Yeah, I first read "no pleasure"! :D
never clicked on something so fast
IKR SHE HASNT POSTED SINCE FOREVER
was about to unsub like 3 times already
I get it... nudge..nudge...nudge
+
I never understood why you'd unsub if you want to see more content. If you stay subbed you might see more. If you unsub you definitely won't. Where is the logic?!
1:00 paradox SOLVED. The area will eventually be the size of a plank length. After that, it will equal nothing and be done.
What a third derivative of position that taxi driver was! I'm glad you're ok.
Ha, I get it, but I won’t explain the joke because I enjoy imagining others being mildly annoyed
Cpg grey just did a video on traffic, are the educational TH-camrs secretly trying to teach us how to drive?
clearly it's not working haha
poisson distribution. whenever an event happens there is a greater probability of a similar event happening shortly after.
s0me1up Conspiracy is the more fun explanation.
They're prepping us up to prevent a future where humans need not apply.
Also Just Between Us uploaded something about driving while distracted yesterday 😄
HOLY VIHART I LOVE YOU
What?? Kittydog, you like vihart!? UwU
Sfs Aviation I’m not a fan of the furry community but calling someone disgusting and especially in all caps is terrible of you. Please keep in mind we’re all human.
ZOLAA
Holy mother of god how the frick can I enjoy this but not understand a thing?
She's entertaining.
I know right?
How do you not understand this? This is pre-calculus, Jesus Christ on barbecue stick. This should be MANDATORY for ANY DRIVER.
I'll explain. The long pedal that makes the loud vroomy noises controls the second derivative of following distance, and is also the first derivative of crashing damage. It only operates in the positive direction. The fat wide pedal does very much the same, but only operates in the negative direction.
The spinny thing you sit under controls the first derivative of theta.
And if it rains really hard and you're going too fast, all of these things will start to act on their own derivative instead.
I seriously doubt that everyone needs to know calculus before being allowed to drive. Rather, they should just know to do A to achieve B. Let the scientists and mathematicians know the innards and complexities, while you tell more simple folk to break earlier and have fun. You don't need to know formulae and theory to practice it.
This was a really interesting video! I think another way to look at it could be from a physics perspective - when you brake on wet pavement vs. dry, the coefficient of friction is lower, so the force acting on your car to decelerate it would decrease. An interesting thing here is that if you slam on the brakes so that they skid, the force on the car would be kinetic friction instead of static, so it would actually take a longer time to stop than if you eased on the brakes making sure that the wheels don't slide along the road. Of course, finding out the exact coefficients of friction is impossible on a practical level and they vary between roads, and then when it boils down, the effects are pretty much the same as in your video.
On the other hand, if you do know your car's rate of deceleration and its original speed, you can figure out exactly how far it will travel before stopping before you hit the brakes.
Part 2!, the prophecy!, finally!, Vihart promisses to teach us more!
Happy 10^6 subscribers!
Oh nice, she did hit 1mil :)
I like your clever way of putting it :)
Chaz Evansdale I couldn't think of a more creative way to do it.
I think she used have over 2 mil in 2012
Arpit Bharti wat. I need to check this...
I checked social blade, and this seems to be the first time she's reached 1 million. At least since 2012, when she only had 100k.
+
yes !! i get so excited when you upload !
More drivers should take the time out of their day to watch this video! The math involved makes it easy to see how to be safer whilst driving in the rain. What I found the most fascinating was how slowing down won't necessarily make driving in the rain any safer. I was confused when they started breaking down the distance and speed using a line, but after watching it a second time, the illustration is more clear to me. This video inspired to think more mathematically about my driving. It caused me to also consider the effects of making more people think this way about driving in the rain and how it would make the roads a safer place.
I missed this kind of thing. I never realized it until it was gone, then reappeared today.
The trick to driving in the rain is to shout ascending prime numbers into the clouds until you reach your destination. This way, the rain will understand that no matter how hard it tries, it'll never amount to what you are, and will leave you alone out of embarrassment.
YES THANK YOU VIHART THIS VIDEO MADE MY DAY I'VE BEEN WAITING FOR SO LONG
Even though you don't upload as much, you're still one of my favs :)
attach backward facing rockets that fire when you SLAM the breaks!
won't they burnl the person on the crosswalk?
Don't place them at the front
It's been so long since she's uploaded a video! Thank you so much, Vi!
yay! another series 😊
hexaflexagons!!!!! hexaflexamexagon!
I liked the hexaflexagons 😁😁😁
Behold the mighty hexaflexamexabexacexadexafexagexajexakexalexamexanexapexaqexarexasexatexavexawexayexazexagon
You said ''mexa' twice. Otherwise quite funny.
Which brings to question, why do so many things covered in driver's ed use esitmated distance rather than time? It's usually easier to judge 4 seconds for the speed you're traveling than 150ft (or whatever). So it works well if you signal 4 seconds ahead, or give yourself 4 seconds of following space. Also when going on estimates for time, it automatically scales in proportion to the speed you're going.
In Canada we're taught to use no less than a 3-second following distance from other vehicles. That is, if the vehicle in front of you were to instantly stop and you were to keep driving at the same speed, you'd have 3 seconds before you collided with it. That gives you plenty of reaction time if, for example, the other vehicle slams on its brakes -- it also prevents the creation of phantom traffic jams caused by traffic waves. (youtube search: phantom traffic jam)
It used to be distance, it's now typically time.
I'm glad your still alive vi :3
I could only imagine how scared/confused someone would be if they rear ended you.
THE SUSPENSE!!! D:
Seriously though, suuuper glad you made another video, Vi. Each one is a little treasure. Looking forward to part 2!
Can't wait for part two! Nice video!
How is it that watching a Vi Hart herself video can make my day better? I don't know but I do care. Thanks for being here Vi.
You are our treasure. Our - meaning the watchers, math fantasizers and those that listen to the fast but melodic voice that explains the math behind everything that interests her.
a vihart video not in march?
When are the angels descending?
Angels? More like angles... Angles descending at an accelerating rate from the beautiful generative heavenly realm that can only be described as Vi Hart's mind.
99growlithe99
word
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Usually I ignore new videos in my feed, but when I don't, it's usually a video from Vi Hart (or Vsauce, or Veritasium...)
The V3 we need
More like V6, since there is Vsauce 2 and 3, and 2veritasium.
An engine of education!
I think you forgot CGP grey
He doesn't start with V though...
thoughty2? vsauce2? vsauce3? 3blue1brown? numberphile?
I'm so glad you lived to tell the tale and make this video - safe travels
Aww, I love it when you upload
Congrats on 1,000,000!!!!!
Always good to see a new Vi Hart video, and on the day of a calculus exam! How auspicious.
Yay!!!! A new post!!! We all love you ViHart, please keep it up (I love the doodle videos)
This was beautiful. The blurb near the end made my day.
Of course, none of this would happen if cars drove themselves.
Someone saw that CGP Grey video
+
*autos
So excited to see you post. Great video
Loved to see another post... Perfect for teaching calculus to others :)
Aaaahhhhh Rain!!!!!!!!!
This made my day :)
I guess you were crossing on yellow, but basically everyone just has to leave a bit more space in front and also begin to brake earlier and exponentially
This is the most elegant and overcomplicated complaint over terrible drivers I've ever heard.
EVERYONE, OUR MUSICAL MATH QUEEN HAS RETURNED! ALL HAIL THE QUEEN!
Your cars look so gorgeous and cute :3
So glad to see your post, miss you, look forward to your next inspiration without almost being hit by a car.
Is it Pi day already?
Nope, we have to wait 3.14159... Wait.
You know what we should do on Pi Day? Tau Hour.
When's that? Six to eight (6 2 8), of course. But wait, that's two hours, isn't it? Well, that's kinda the point.
+
I had to read it twice, but you are kind of a genius.
Anybody mind explaining?
Finally I love your videos
I love you videos like this. Brings me back to your line logarithm videos.
YAY! NEW VIHART VIDEO FOR THE DAY AFTER I WASN'T IN THE 90% OF MY CLASS THAT FAILED A TEST ON FIRST DEGREE EQUATIONS WITH ONE VARIABLE!
As someone who just took her license, it comes as a pleasant surprise that you just happened to pop up with the first video I have some form of previous knowledge about, regarding the subject you have chosen!
I am really and truly glad your almost doom was just the auspice of your journey into acceleration/deceleration slopes and not your untimely end.
But what about Planck lengths, I'm watching this video at night with low volume so not sure if you already mentioned that but a Planck length is the shortest practical distance that you can go. So eventually you will come to an end of cutting roads in half.
YAAAAY Vi hart video! AND A PART 2 COMING!!! best day ever!
It always makes me happy (or sad, if you're upset) when you upload :)
The calculus we do while driving is subconscious. If it were conscious... traffic would flow at around max of 2MPH all the time.
If 98% of the time, the roads are dry, you quickly learn the subconscious calculus to stop where you need to, no matter what speed you're going. But if a rare condition like rain or snow happens... you'll be in trouble if you're brain is driving on auto-pilot.
This will probably also be a huge problem for self driving cars in the near future... even though they can do calculus "consciously" on the fly... because there are so many variables.
The weight of the car, which affects it's momentum. The quality of the break pads. The tread on the tires. The roughness of the road surface, and the surface tension of the water on the road.
All of that said... the worst drivers I've ever seen, by far, are taxi drivers.
Thanks for making me feel good about math again because I lost hope when I started my first college math in math theory (we call it foundations of mathematics) when all I could do was find derivatives and integrate stuff. Calculus has been bae.
Happy 1 million subscibers Vi Hart :)
🎂🎂🍪🍪CAKE AND COOKIES FOR YOU
So glad you post again
We literally started learning about derivatives in AP Calculus the day you uploaded this
Yay, another Vi video! Also yes, my high-school physics taught me so much more about what happens when I'm driving than the people who taught me to drive. Once you understand how momentum works, you really understand why 60kg me travelling at 1ms^-1 shouldn't mess with a 1t car travelling at 18ms^-1.
Yay! A new Vihart video!!! I adore your videos!
An interesting breakdown of the kind of stuff we do naturally within fractions of a second. Also: it's good to hear an explanation of how simply driving slower doesn't mean shit in wet conditions, it's all about the space you leave yourself and others and how you handle the vehicle. Reporting from Indiana and I can attest that rain destroys the already abysmal traffic flow around here. I think it's just a direct result of poor education in operation because it rains/snows here enough to where it shouldn't be a mystery for anybody.
WHEN IS NEXT TIME
Always love seeing the Pontmercy face in the wild.
+
I hope soon
whenever zeno is mentioned i swoon
And you never hit the ground because there isn't enough time to hit the ground
Delighted to watch again a "classic Vihart":-) Looking forward to part 2, especially, should You tackle different options, to determin the slope, at a given point.
AND THERE'S A FREAKING PART 2! :DDD
lets hope there is
Congrats on 1 million!
Yay, you're not dead!! I love your videos
YESSS NEW UPLOAD i love you
The joke in New Mexico about rain is a few minutes after it starts raining sirens will appear.
lol
trying to understand this with my 5 weeks calc knowledge is a journey (but ah!!!! you're back!!!! new vid!!!!!!!)
Congrats on 1 million!!!!!
This is great! I took Calc last year and loved it!
Yay! A Vi hart video! I was counting down the days till 3/14/17 until I saw this yayayay!!!
Much much bigger issue is when you are on sidewalks and not on crosswalks.
Mainly because stopping or acceleration speed doesn't matter when you drive through a puddle in a high speed..
Nice to see you back to your normal topics of videos :)
How great to see you posting! :)
It's hard to tell what I like most about Vi Hart -- her cool drawings, her great content or her beautiful voice...
What I love most about Vihart is that she can talk about mathematics in such a romantic way by giving the concrete or asphalt example of calculus applied to driving. Math ceases to be a confusing abstract concept to me only until l have to do the math myself.
Your awesome. Thank you for the great videos.
Go Vi Hart!!! PREACH!!! Another great vid lookin' at slopes lol! can't wait for part 2! ^_^
You're back!
I really love Hermione Granger and want to be her. Mentioning this fact to my friend in passing, she told me I wasn't smart enough to to be her. My intelligence is really something I value, and I was super hurt, even though she was just being honest. Now I'm doubting my whole image of myself. Any advice?
🙁
This world runs on work ethic. Hermione was smart because she worked hard at it and you can too.
I like that you applied math in a frequently occurring real life scenario. Some of the physics were confusing because I have yet to take a physics class. This inspires me to begin learning to drive because it gives me an idea as to how simple it can be. I like that it made a somewhat confusing driving scenario simple and understandable.
The physics of a car stopping is only part of it. Something not mentioned (and CGP Grey didn't mention in his last video) is that most of it is actually human reaction time. Yellow lights help, but at high distances (like some places where you drive over 50 with stoplights) it can be hard to discern if you're too close to stop in time (without completely slamming your brakes) or not. By the time some people process this, they're already too far to stop and are running a red light.
Of course, some people just aren't paying attention, and that's the worst. I've been rear ended while stopped (it was red before I ever got to it) because someone behind me wasn't paying attention.
Acceleration is not change in speed over time but change in velocity over time. This makes really big difference if you think of circular motion of constant speeds - by your definition, the object in this motion experiences no acceleration what so ever. You could practically think of acceleration this way in motion along a line, but it is deceptive - if you think of acceleration of say 1 (m/s)/s, but you start with velocity of -1 m/s, then the chage in speed changes its behavior after the first second - from decreasing the speed to increasing it.
In this particular case, the direction of motion doesn't change so it's okay to use either speed or velocity. However, there are many situations where it would matter.
Somewhat off topic but this reminded me of my Real Analysis professor. He used to always say that cops should use the Mean Value Theorem (of derivatives) to catch people speeding xD
There's going to be another video!? The youtube gods have blessed us
"For the first time in foreverrrr! I actually got here earlyyy!"
We missed you Vi
SHE'S BACK!!!
*sounds the trumpets, rolls the red carpet*
Happy to see Vi Hart making videos again.
I've never thought about acceleration and deceleration like this before! While it is confusing, starts to make sense when you think about. I like how the graph showed different conditions and how the conditions affect acceleration and deceleration.
Vi videos always make my day ♡
yay!!!! calculus!!!!! I have been waiting for this day.
oh man, i just still LOVE your voice, and the stuff it's telling is very interesting and fun too! best of 2 worlds!!!!!
also, oh man the anti-pi rant is over 2 years old.... time flies...
I love your sense of humor!!! Hope you come to Mexico one day to see one of your conferences.. blessings :)