This Will Be Your Favorite Physics Problem

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Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information.

#math #brithemathguy #physics

[BriTheMathGuy]

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[GlorifiedTruth]

I've just one lap in one time period. Now, in order to double my average speed, I'd need to run 2 laps total in one time period, which means I'd have to run the second lap in zero seconds. That's my "real world" interpretation of the algebra. (Not "real world, " though, because in real life I can't run one lap, much less two.)

[SagaTympana]

The algebra is good, but you can work through it logically to identify the impossibility as well. For twice the average speed, you need to go twice as far in the same amount of time. Since you’ve definitionally gone half the distance already, you need to add the second lap without changing the time at all to produce that result, exactly what you showed algebraically.

[BriTheMathGuy]

Veritasium posed this question on YouTube years ago so this is my (very late) video response.

If you didn't enjoy this video make sure to give it a dislike and have a wonderful day!

[Boringpenguin]

iirc Veritasium also did a video about this problem.
It's really deceptive at first, but the "trap" becomes clear once you've written down the math step by step. Great video :)

[moskthinks]

Generally, when averaging velocities, rather than the arithmetic mean [(a+b)/2], you use the harmonic mean [2/(1/a+1/b)]. Plugging V1 and V2, we get 1/V2 = 0, which is impossible.

[magicmulder]

It’s also easy to understand without much calculation.
If you run the first round in time T (and thus 2 rounds in time 2T) and the end result is supposed to be running 2 rounds in time T (twice as fast as running 2 rounds in time 2T) so you realize you have already used up that time in your first round.

[law]

This problem comes from the wrong understanding that people have about the average speed.
Avg speed = total distance/total time, not the mean of the speeds over different intervals.

[alexmorrison-ml]

I've never been so unsatisfied with the answer to a riddle...

[blaze-shuriken]

Why don't they put these problems on the tests?

[Osirion]

If the track is for example, 1km long and you complete that lap in 1 hour
Then, for having an average speed of 2km/h ( so twice the speed of the first lap ) You'd need to do 2km in 1h ( because 2km/h = 2km in 1 hour ez logic )
So, since the track is 1km, you'd have run 2km total after completing the lap a second time. So, knowing you completed 2km, you'd have to have done it in an hour, which is impossible since the first lap already took you 1 hour. :) ( So essentially this shows that the second lap would have to be ran in 0 seconds, basically saying that the speed of the second lap would need to be infinity )

[jordisimon]

The average of this can be taken in two ways: In distance and in time. In time it is impossible to double your initial average, but in distance you certainly can (3V1)!

[GodzillaFreak]

I like how Dr. Lisle just brushes over this in his distant starlight video

[Daenym]

Sorry, my favorite simple physics problem is:
"What is the minimum amount of energy I can expend on this task?"

[yahligilboa]

Nice diffrentiation between "average velocity" and "average velocity values", i really liked it and didnt notice it at first!

[TrimutiusToo]

My physics degree is showing. The first attempt at solution from video didn't even come to mind, i did it the right way from the start

[ojasapratim]

I do hard problem based on integral and differential calculus every day, can’t do this one. I want to die….

[sphakamisozondi]

I think Einstein was also given his problem but instead of Runnin in a circle, his question was about going up a hill and travelling down from the peak

[jamirimaj]

The first method would work if instead of distance/time, it is time/distance instead, like seconds per meter.

[stonezoo]

Infact any number greater than or equal to two will give such a contradiction (if n>2, the times will come out to be negative)