A trip through space to calculate distance - Heather Tunnell

154,836 views ใƒป 2013-09-06

TED-Ed


ไธ‹ใฎ่‹ฑ่ชžๅญ—ๅน•ใ‚’ใƒ€ใƒ–ใƒซใ‚ฏใƒชใƒƒใ‚ฏใ™ใ‚‹ใจๅ‹•็”ปใ‚’ๅ†็”Ÿใงใใพใ™ใ€‚

็ฟป่จณ: Akiko Kawagoe ๆ กๆญฃ: Tomoyuki Suzuki
00:06
Do you have a friend or a sibling
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ใ‚ใชใŸใฎๅ‹้”ใ‚„ๅ…„ๅผŸๅง‰ๅฆนใซ
00:07
that's always competing with you
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ใ„ใคใ‚‚ ่ชฐใŒไธ€็•ช้€Ÿใ„ใ‹ ๅ‹่ฒ ใ‚’ใ—ใ‹ใ‘ใฆใใ‚‹ไบบใฏใ„ใพใ›ใ‚“ใ‹๏ผŸ
00:09
to see who's the fastest?
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00:11
Our alien friends Bleebop and Mark
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ๅฎ‡ๅฎ™ไบบใฎๅ‹้” ใƒ–ใƒชใƒผใƒœใƒƒใƒ—ใจใƒžใƒผใ‚ฏใ‚‚
00:13
are having the same debate
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่‡ชๅˆ†ใŸใกใŒๆ”น่‰ฏใ—ใŸใƒญใ‚ฑใƒƒใƒˆใฎ
00:14
with their custom-built rockets,
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ใฉใกใ‚‰ใŒ้€Ÿใ„ใ‹ใ‚’่ญฐ่ซ–ใ—ใฆใ„ใพใ™
00:16
and they've asked us
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ใใ“ใง ็งใŸใกใŒ
00:17
to be the judge of a space race to their moon.
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ๆœˆใธใฎๅฎ‡ๅฎ™ใƒฌใƒผใ‚นใฎๅฏฉๅˆคใ‚’ ไปปใ•ใ‚Œใ‚‹ใ“ใจใซใชใ‚Šใพใ—ใŸ
00:20
The only problem is that they are starting
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ๅ”ฏไธ€ใฎๅ•้กŒใฏ
ๅฝผใ‚‰ใŒใใ‚Œใžใ‚Œ็•ฐใชใ‚‹ๆƒ‘ๆ˜Ÿใ‹ใ‚‰ ๅ‡บ็™บใ™ใ‚‹ใ“ใจใงใ™
00:22
from different asteroids.
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00:23
Bleebop is on an asteroid 240 miles from the moon,
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ใƒ–ใƒชใƒผใƒœใƒƒใƒ—ใฏ ๆœˆใ‹ใ‚‰240ใƒžใ‚คใƒซ้›ขใ‚ŒใŸๆƒ‘ๆ˜Ÿใ‹ใ‚‰
00:27
and Mark is on one 150 miles away.
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ใƒžใƒผใ‚ฏใฏ 150ใƒžใ‚คใƒซ้›ขใ‚ŒใŸๆƒ‘ๆ˜Ÿใ‹ใ‚‰ ๅ‡บ็™บใ—ใพใ™
00:30
Don't worry, it's not rocket science.
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ๅฟƒ้…ใฏใ„ใ‚Šใพใ›ใ‚“ ้ซ˜ๅบฆใซ้›ฃใ—ใ„ๅ•้กŒใงใฏใ‚ใ‚Šใพใ›ใ‚“ใ‚ˆ
00:32
Solving this equation is as simple as DIRT.
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ใ“ใฎๆ–น็จ‹ๅผใ‚’่งฃใใซใฏ ใ€ŒDIRTใ€ ใŸใ ใใ‚Œใ ใ‘ใงใ™
00:36
We can decide who the winner is
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ๅ‹่€…ใ‚’ๆฑบใ‚ใ‚‹ใซใฏ
00:37
using the D=RT formula, or DIRT.
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ใ€ŒD=RTใ€ใฎๅ…ฌๅผ ใคใพใ‚Šใ€ŒDIRTใ€ ใ‚’ไฝฟใˆใฐใ‚ˆใ„ใฎใงใ™
00:41
This stands for distance equals rate times time.
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ใ“ใ‚Œใฏใ€Œ่ท้›ข๏ผ้€Ÿๅบฆร—ๆ™‚้–“ใ€ใฎใ“ใจใงใ™
00:44
In the case of Bleebop and Mark,
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ใƒ–ใƒชใƒผใƒœใƒƒใƒ—ใจใƒžใƒผใ‚ฏใฎๅ ดๅˆ
00:46
we will only know the distance they traveled
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ๅฝผใ‚‰ใŒใ‚ดใƒผใƒซใ™ใ‚‹ใพใงใซใ‹ใ‹ใฃใŸ
00:48
and the time it took for them
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่ท้›ขใจๆ™‚้–“ใ ใ‘ใŒ
00:50
to get to the finish line.
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ๅˆ†ใ‹ใฃใฆใ„ใพใ™
00:51
It'll be up to us to find the rate
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้€Ÿๅบฆใ‚’่ชฟในใฆๅ‹่€…ใ‚’ๆฑบใ‚ใ‚‹ใ“ใจใŒ
00:52
and who is faster.
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็งใŸใกใฎๆ‰‹ใซใ‹ใ‹ใฃใฆใ„ใพใ™
00:54
Let's turn to the race now
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ใงใฏ ใƒฌใƒผใ‚นใซๅ‘ใ‹ใ„ใพใ—ใ‚‡ใ†
00:56
and see what information we get.
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ใฉใ‚“ใชๆƒ…ๅ ฑใŒๅพ—ใ‚‰ใ‚Œใ‚‹ใงใ—ใ‚‡ใ†ใ‹
00:58
Three,
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๏ผ“
00:59
two,
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๏ผ’
01:00
one,
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๏ผ‘
01:01
blast off!
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็™บๅฐ„๏ผ
01:03
Bleebop and Mark's rockets go zipping
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ใƒ–ใƒชใƒผใƒœใƒƒใƒ—ใจใƒžใƒผใ‚ฏใฎใƒญใ‚ฑใƒƒใƒˆใฏ
01:05
across the galaxy towards their moon,
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ๅ‹ขใ„ใ‚ˆใ้Š€ๆฒณใ‚’ๆจชๅˆ‡ใ‚Š ๆœˆใซๅ‘ใ‹ใฃใฆใ„ใพใ™
01:07
dodging clunky meteorites
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ใ‚ดใƒ„ใ‚ดใƒ„ใ—ใŸ้š•็Ÿณใ‚„
01:08
and loopy space buggies.
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ใƒ˜ใƒณใƒ†ใ‚ณใชๅฎ‡ๅฎ™ใฎไน—ใ‚Š็‰ฉใ‚’ ใ•ใฃใจใ‚ˆใ‘ใพใ™
01:11
After a few close calls with a wandering satellite,
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ไฝ•ๅบฆใ‹ ๅฝทๅพจใ†่ก›ๆ˜Ÿใ‚’้–“ไธ€้ซชใงใ‹ใ‚ใ—ใŸๅพŒ
01:13
Mark arrives first in two hours,
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ๆœ€ๅˆใซ ใƒžใƒผใ‚ฏใŒ๏ผ’ๆ™‚้–“ๅพŒใซๅˆฐ็€ใ—
01:16
and Bleebop gets there one hour later.
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ใƒ–ใƒชใƒผใƒœใƒƒใƒ—ใฏ ใใฎ๏ผ‘ๆ™‚้–“ๅพŒใซๅˆฐ็€ใ—ใพใ—ใŸ
01:19
Looks like Mark has the faster rocket,
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ใƒžใƒผใ‚ฏใฎใƒญใ‚ฑใƒƒใƒˆใฎๆ–นใŒ ้€Ÿใใ†ใซ่ฆ‹ใˆใพใ™ใŒ
01:21
but let's check out the results with our DIRT equation.
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ใ€ŒDIRTใ€ๆ–น็จ‹ๅผใง ็ตๆžœใ‚’่ชฟในใฆใฟใพใ—ใ‚‡ใ†
01:24
Begin by setting up a chart.
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ใพใš ่กจใ‚’ๆบ–ๅ‚™ใ—ใพใ—ใ‚‡ใ†
01:26
Make four columns and three rows.
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๏ผ”ๅˆ—ร—๏ผ“่กŒใฎ่กจใ‚’ไฝœใ‚Šใพใ™
01:28
Use DIRT to remember what to fill in.
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ใ€ŒDIRTใ€ใ‚’ไฝฟใฃใฆ ่กจใซไฝ•ใŒๅ…ฅใ‚‹ใ‹่€ƒใˆใพใ—ใ‚‡ใ†
01:31
Each rocket will have information
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ใฉใกใ‚‰ใฎใƒญใ‚ฑใƒƒใƒˆใ‚‚
01:33
for distance, rate, and time.
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่ท้›ข ้€Ÿๅบฆ ๆ™‚้–“ใฎๆƒ…ๅ ฑใŒ ๅพ—ใ‚‰ใ‚Œใ‚‹ใงใ—ใ‚‡ใ†
01:35
Mark's rocket went 150 miles,
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ใƒžใƒผใ‚ฏใฎใƒญใ‚ฑใƒƒใƒˆใฏ 150ใƒžใ‚คใƒซใ‚’้ฃ›ใณใพใ—ใŸ
01:38
we don't know the rate,
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้€Ÿๅบฆใฏๅˆ†ใ‹ใ‚Šใพใ›ใ‚“
01:39
and he got there in 2 hours.
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ใใ—ใฆ ใƒžใƒผใ‚ฏใฏ๏ผ’ๆ™‚้–“ใงๅˆฐ็€ใ—ใพใ—ใŸ
01:41
Bleebop's rocket went 240 miles,
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ใƒ–ใƒชใƒผใƒœใƒƒใƒ—ใฎใƒญใ‚ฑใƒƒใƒˆใฏ 240ใƒžใ‚คใƒซใ‚’้ฃ›ใณใพใ—ใŸ
01:44
we don't know the rate,
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้€Ÿๅบฆใฏๅˆ†ใ‹ใ‚Šใพใ›ใ‚“
01:45
and the time is 1 hour after Mark,
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ใ‹ใ‹ใฃใŸๆ™‚้–“ใฏ ใƒžใƒผใ‚ฏใ‚ˆใ‚Š๏ผ‘ๆ™‚้–“ๅพŒใ ใฃใŸใฎใง
01:48
or 3 hours.
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๏ผ“ๆ™‚้–“ใงใ™
01:49
Because we don't know Mark or Bleebop's rate,
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ใƒžใƒผใ‚ฏใจใƒ–ใƒชใƒผใƒœใƒƒใƒ—ใฎ ้€ŸๅบฆใŒๅˆ†ใ‹ใ‚‰ใชใ„ใฎใง
01:52
that number is going to be a variable
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ใใ‚Œใžใ‚Œใฎๆ–น็จ‹ๅผใซ
01:54
in each equation,
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ๅค‰ๆ•ฐใจใ—ใฆ
01:55
which we'll represent with x.
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ใ€Œxใ€ใ‚’็ฝฎใใพใ™
01:57
We'll solve the equation
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ใ“ใฎๆ–น็จ‹ๅผใ‚’่งฃใ„ใฆ
01:58
for the variable to find its value.
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ๅค‰ๆ•ฐใฎๅ€คใ‚’่ฆ‹ใคใ‘ใพใ—ใ‚‡ใ†
02:01
Mark finished first,
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ใƒžใƒผใ‚ฏใŒๅ…ˆใซใ‚ดใƒผใƒซใ—ใŸใฎใง
02:02
so start with his rocket.
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ๅฝผใฎใƒญใ‚ฑใƒƒใƒˆใ‹ใ‚‰่€ƒใˆใฆใฟใพใ—ใ‚‡ใ†
02:04
Remembering DIRT, write down D=RT.
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ใ€ŒDIRTใ€ใ‚’ๆ€ใ„ๅ‡บใ—ใชใŒใ‚‰ ใ€Œ่ท้›ข๏ผ้€Ÿๅบฆร—ๆ™‚้–“ใ€ใจๆ›ธใใพใ™
02:07
150 miles equals x times 2 hours.
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150ใƒžใ‚คใƒซ๏ผx ร—๏ผ’ๆ™‚้–“
02:11
Divide both sides by 2 hours.
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ไธก่พบใ‚’๏ผ’ๆ™‚้–“ใงๅ‰ฒใ‚Šใพใ™
02:13
This will leave x isolated
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xใŒๆ–น็จ‹ๅผใฎๅณ่พบใซๆฎ‹ใ‚Šใพใ™
02:15
on the right side of the equation.
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02:17
150 miles divided by 2 hours
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150ใƒžใ‚คใƒซใ‚’๏ผ’ๆ™‚้–“ใงๅ‰ฒใ‚‹ใจ
02:19
is 75 miles over 1 hour.
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๏ผ‘ๆ™‚้–“ใ‚ใŸใ‚Š75ใƒžใ‚คใƒซ
02:22
Mark's rate is 75 miles per hour.
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ใƒžใƒผใ‚ฏใฎ้€Ÿๅบฆใฏ ๆ™‚้€Ÿ75ใƒžใ‚คใƒซใจใชใ‚Šใพใ™
02:25
That's what mph means.
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ใ“ใ‚ŒใŒmph๏ผˆใƒžใ‚คใƒซๆฏŽๆ™‚๏ผ‰ใงใ™
02:26
It's the amount of miles over one hour.
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๏ผ‘ๆ™‚้–“ใ‚ใŸใ‚Šใซ้€ฒใ‚€ ่ท้›ข๏ผˆใƒžใ‚คใƒซ๏ผ‰ใฎใ“ใจใงใ™
02:29
Still think Mark is faster?
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ใพใ ใƒžใƒผใ‚ฏใฎๆ–นใŒ้€Ÿใ„ใจๆ€ใ„ใพใ™ใ‹๏ผŸ
02:31
Let's set up the same equation for Bleebop and see.
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ใงใฏ ใƒ–ใƒชใƒผใƒœใƒƒใƒ—ใซใคใ„ใฆ ๅŒใ˜ๆ–น็จ‹ๅผใง่€ƒใˆใฆใฟใพใ—ใ‚‡ใ†
02:34
D=RT
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ใ€Œ่ท้›ข๏ผ้€Ÿๅบฆร—ๆ™‚้–“ใ€
02:36
240 miles equals x times 3 hours.
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240ใƒžใ‚คใƒซ๏ผx ร—๏ผ“ๆ™‚้–“
02:39
Divide both sides by 3 hours.
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ไธก่พบใ‚’๏ผ“ๆ™‚้–“ใงๅ‰ฒใ‚Šใพใ™
02:42
This will leave x isolated
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xใŒๆ–น็จ‹ๅผใฎๅณ่พบใซๆฎ‹ใ‚Šใพใ™
02:43
on the right side of the equation.
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02:46
240 miles divided by 3 hours
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240ใƒžใ‚คใƒซใ‚’๏ผ“ๆ™‚้–“ใงๅ‰ฒใ‚‹ใจ
02:49
is 80 miles over 1 hour.
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๏ผ‘ๆ™‚้–“ใ‚ใŸใ‚Š80ใƒžใ‚คใƒซ
02:50
Bleebop's rate is 80 miles per hour.
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ใƒ“ใƒผใƒœใƒƒใƒ—ใฎ้€Ÿๅบฆใฏ ๆ™‚้€Ÿ80ใƒžใ‚คใƒซใจใชใ‚Šใพใ™
02:53
Wow, even though Bleebop got there one hour later,
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ใŠใ‰๏ผ ใƒ–ใƒชใƒผใƒœใƒƒใƒ—ใฏ ๏ผ‘ๆ™‚้–“้…ใ‚Œใงๅˆฐ็€ใ—ใŸใฎใซ
02:56
it turns out he had the faster rocket.
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ๅฝผใฎใƒญใ‚ฑใƒƒใƒˆใฎๆ–นใŒ้€Ÿใ„ใจๅˆ†ใ‹ใ‚Šใพใ—ใŸใ‚ˆ
02:59
Mark seems pretty upset,
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ใƒžใƒผใ‚ฏใฏใ‚ฌใƒƒใ‚ซใƒชใ—ใฆใ„ใ‚‹ใ‚ˆใ†ใงใ™ใŒ
03:00
but with aliens, you can never really tell.
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ๅฎ‡ๅฎ™ไบบใงใ™ใ‹ใ‚‰ ๆœฌๅฝ“ใฎใจใ“ใ‚ใฏๅˆ†ใ‹ใ‚Šใพใ›ใ‚“ใ‚ˆใญ
03:03
Thanks to DIRT, you now know how to calculate
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ใ€ŒDIRTใ€ใฎใŠใ‹ใ’ใง ใ‚‚ใ†่จˆ็ฎ—ใฎๆ–นๆณ•ใŒๅˆ†ใ‹ใ‚Šใพใ—ใŸใญ
03:05
distance,
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่ท้›ข
03:06
rate,
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03:06
and time.
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้€Ÿๅบฆ
ๆ™‚้–“
03:07
In what other situations
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ไป–ใฎ็Šถๆณใงใ‚‚
03:08
can you use the distance formula?
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ใ“ใฎ่ท้›ขใฎๅ…ฌๅผใŒไฝฟใˆใ‚‹ใงใ—ใ‚‡ใ†ใ‹๏ผŸ
03:11
You don't even need to be watching a space race.
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ๅฎ‡ๅฎ™ใƒฌใƒผใ‚นใชใ‚“ใฆ่ฆ‹ใ‚‹ๅฟ…่ฆใฏใ‚ใ‚Šใพใ›ใ‚“
03:13
As long as you know two pieces of information
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ใ€Œ่ท้›ข๏ผ้€Ÿๅบฆร—ๆ™‚้–“ใ€ใจใ„ใ†ๅ…ฌๅผใฎใ†ใก
03:15
for the formula D=RT,
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๏ผ’ใคใฎๆƒ…ๅ ฑใŒๅˆ†ใ‹ใ‚Œใฐ
03:18
you can calculate any moving vehicle or object.
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ๅ‹•ใ„ใฆใ„ใ‚‹ไน—ใ‚Š็‰ฉใ‚„ใƒขใƒŽใชใฉ ไฝ•ใงใ‚‚่จˆ็ฎ—ใงใใพใ™
03:21
Now, the next time you're in a car,
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ใ“ใ‚ŒใงไปŠๅบฆ ่ปŠใซไน—ใ‚‹ๆ™‚ใซ
ๆญฃ็ขบใชๅˆฐ็€ๆ™‚้–“ใ‚„
03:23
you can let your friends know
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03:24
exactly when you'll be arriving,
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ใฉใฎใใ‚‰ใ„ใฎ้€Ÿใ•ใงๅ‘ใ‹ใฃใฆใ„ใ‚‹ใ‹
03:25
how fast you're going,
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ใ‚ใ‚‹ใ„ใฏ ็งปๅ‹•ใ™ใ‚‹่ท้›ขใ‚’
03:27
or the distance you'll travel.
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ๅ‹้”ใซ็Ÿฅใ‚‰ใ›ใ‚‹ใ“ใจใŒใงใใพใ™ใญ
03:28
It's as simple as DIRT.
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ใ€ŒDIRTใ€ ใŸใ ใใ‚Œใ ใ‘ใงใ™
ใ“ใฎใ‚ฆใ‚งใƒ–ใ‚ตใ‚คใƒˆใซใคใ„ใฆ

ใ“ใฎใ‚ตใ‚คใƒˆใงใฏ่‹ฑ่ชžๅญฆ็ฟ’ใซๅฝน็ซ‹ใคYouTubeๅ‹•็”ปใ‚’็ดนไป‹ใ—ใพใ™ใ€‚ไธ–็•Œไธญใฎไธ€ๆต่ฌ›ๅธซใซใ‚ˆใ‚‹่‹ฑ่ชžใƒฌใƒƒใ‚นใƒณใ‚’่ฆ‹ใ‚‹ใ“ใจใŒใงใใพใ™ใ€‚ๅ„ใƒ“ใƒ‡ใ‚ชใฎใƒšใƒผใ‚ธใซ่กจ็คบใ•ใ‚Œใ‚‹่‹ฑ่ชžๅญ—ๅน•ใ‚’ใƒ€ใƒ–ใƒซใ‚ฏใƒชใƒƒใ‚ฏใ™ใ‚‹ใจใ€ใใ“ใ‹ใ‚‰ใƒ“ใƒ‡ใ‚ชใ‚’ๅ†็”Ÿใ™ใ‚‹ใ“ใจใŒใงใใพใ™ใ€‚ๅญ—ๅน•ใฏใƒ“ใƒ‡ใ‚ชใฎๅ†็”ŸใจๅŒๆœŸใ—ใฆใ‚นใ‚ฏใƒญใƒผใƒซใ—ใพใ™ใ€‚ใ”ๆ„่ฆ‹ใƒปใ”่ฆๆœ›ใŒใ”ใ–ใ„ใพใ—ใŸใ‚‰ใ€ใ“ใกใ‚‰ใฎใŠๅ•ใ„ๅˆใ‚ใ›ใƒ•ใ‚ฉใƒผใƒ ใ‚ˆใ‚Šใ”้€ฃ็ตกใใ ใ•ใ„ใ€‚

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