/sci/ - Science & Math » Thread #11745254

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I still don't understand

Anonymous Sun 31 May 12:45:33 2020 No.11745254 View Reply Original Report

Quoted By: >>11745389 >>11750564 >>11752244 >>11752251

>race car does one lap around a 1-mile track, averaging 30mph
>how fast does the car have to go to average 60mph across both laps?

The answer is not 90, it's that it's impossible because even past the speed of light it still won't reach that average. But why? I don't get it.

Anonymous

Anonymous Sun 31 May 2020 13:12:05 No.11745389 Report

Quoted By:

>>11745254
Dude, how old are you? That's elementary school tier.

v=d/t (speed is distance covered per unit of time)

Since: 30miles/h=1mile/t on the first lap
the car needed 1/30 of an hour (2 minutes) for one mile.
You want to average 60mph on two miles, under the condition it needed 1/30 of an hour for one mile. Therefore, 60miles/h=2miles/t -> t=1/30h.
That means: you have to cover 2 miles in 2 minutes to average 60mph.

Since you already needed two minutes for the first mile, you had to drive the second mile at an infinite speed to make it in absolutely no time, which is of course impossible.

Anonymous

Anonymous Sun 31 May 2020 22:27:13 No.11750564 Report

Quoted By: >>11750806

>>11745254
So two laps of a 1 mile track is 2 miles overall. Two miles at a pace of 60 mph take 1/30 of an hour. The first lap/the first mile at 30 mph takes 1/30 hour to complete. You already spent 1/30 of an hour on your first lap so you can no longer make 2 miles in an 1/30 of an hour like you need to.

Anonymous

Anonymous Sun 31 May 2020 23:27:25 No.11750806 Report

Quoted By: >>11750817 >>11750865

>>11750564
This is actually wrong if we starting using relativistic speeds and the clock is inside the car

Anonymous

Anonymous Sun 31 May 2020 23:32:03 No.11750817 Report

Quoted By: >>11750819

>>11750806
>relativistic speeds
30mph,
60mph...
Sure, dude, sure...

Anonymous

Anonymous Sun 31 May 2020 23:32:39 No.11750819 Report

Quoted By:

>>11750817
bro the planet is moving relativistically if u think about it

Anonymous

Anonymous Sun 31 May 2020 23:50:50 No.11750865 Report

Quoted By:

>>11750806
>and the clock is inside the car
Shut the fuck up you fucking nerd. Literally no car race in the world clocks a car using a clock built into the car.

Anonymous

Anonymous Mon 01 Jun 2020 13:22:33 No.11752238 Report

Quoted By: >>11752242

think of it like this: car A goes 1mph, car B goes 2mph. After one hour has passed, A has made one lap while B has made 2 laps. Now you ask the question: In the next hour, how fast does car A have to race around the track so that it makes 2 laps in the same time B did?

Anonymous

Anonymous Mon 01 Jun 2020 13:28:04 No.11752242 Report

Quoted By: >>11752255

>>11752238
>In the next hour, how fast does car A have to race around the track so that it makes 2 laps in the same time B did?
B did 2 laps (miles) in 1 hour so A has to go 2 mph in the next hour to make 2 laps in 1 hour.

Anonymous

Anonymous Mon 01 Jun 2020 13:33:02 No.11752244 Report

Quoted By:

>>11745254
this is a good introduction to limits

Anonymous

Anonymous Mon 01 Jun 2020 13:40:13 No.11752251 Report

Quoted By:

>>11745254
you mean it did 1 lap at 30 mph and is doing another?
to finish in 60 mph average it would need to do 2 laps in 2miles/60mph=1/30 hours. it finished the first lap in 1mile/30mph=1/30hours. its impossible to get 60 mph average across both since the time already ran out.

this is if we're talking speed averaged over time, if we're averaging the speed over displacement we get (1mile*30mph+1mile/Xmph)/2miles =60mph
X=90mph

Anonymous

Anonymous Mon 01 Jun 2020 13:41:45 No.11752255 Report

Quoted By:

>>11752242
no, they start at the same time and after one hour car A has passed the finish line once while car B has passed it twice. Its impossible for car A because at the exact same time of the start of hour2/round2 for car A, car B crosses the line for the second time.

Ok think of it like this, one mile lap, one lap race, car B drives twice as fast as car A, Car B crosses the finish line. How fast does car A have drive to win the race at the time car B has won the race?

Anonymous

Anonymous Mon 01 Jun 2020 21:48:04 No.11753385 Report

Quoted By: >>11753405

Another perspective: to get the average speed of two speeds over the same distance you must use the harmonic mean of the speeds.
So avg = 2/(1/s1+1/s2)
i.e. 60 = 2/(1/30+1/s2)
2/60 = 1/30 + 1/s2
1/s2 = 2/60 - 1/30 = 0
so s2 would have to be 1/0 which is impossible

Anonymous

Anonymous Mon 01 Jun 2020 22:00:06 No.11753405 Report

Quoted By:

>>11753385
and of course if the required average speed were still higher you would need a negative speed on the 2nd lap (drive backwards maybe)

Anonymous

Anonymous Tue 02 Jun 2020 00:19:54 No.11753707 Report

Quoted By:

now someone tell me how the fuck I can relate this to achilles and the turtle paradox. Even though I didn't explain it like this earlier I feel like its something like this, but I gotta be honest reading the question at first yesterday I was kinda suprised.. feels counter-intuitive as fuck, but the math was really easy.

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