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1.2 Physical quantities and units  (Page 5/18)

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Approximate values of length, mass, and time
Lengths in meters Masses in kilograms (more precise values in parentheses) Times in seconds (more precise values in parentheses)
10 − 18 Present experimental limit to smallest observable detail 10 − 30 size 12{"10" rSup { size 8{ - "30"} } } {} Mass of an electron 9 . 11 × 10 − 31  kg size 12{9 "." "11" times "10" rSup { size 8{ - "31"} } `"kg"} {} 10 − 23 size 12{"10" rSup { size 8{ - "23"} } } {} Time for light to cross a proton
10 − 15 size 12{"10" rSup { size 8{ - "15"} } } {} Diameter of a proton 10 − 27 size 12{"10" rSup { size 8{ - "27"} } } {} Mass of a hydrogen atom 1 . 67 × 10 − 27  kg size 12{1 "." "67" times "10" rSup { size 8{ - "27"} } `"kg"} {} 10 − 22 size 12{"10" rSup { size 8{ - "22"} } } {} Mean life of an extremely unstable nucleus
10 − 14 size 12{"10" rSup { size 8{ - "14"} } } {} Diameter of a uranium nucleus 10 − 15 size 12{"10" rSup { size 8{ - "15"} } } {} Mass of a bacterium 10 − 15 size 12{"10" rSup { size 8{ - "15"} } } {} Time for one oscillation of visible light
10 − 10 size 12{"10" rSup { size 8{ - "10"} } } {} Diameter of a hydrogen atom 10 − 5 size 12{"10" rSup { size 8{ - 5} } } {} Mass of a mosquito 10 − 13 size 12{"10" rSup { size 8{ - "13"} } } {} Time for one vibration of an atom in a solid
10 − 8 size 12{"10" rSup { size 8{ - 8} } } {} Thickness of membranes in cells of living organisms 10 − 2 size 12{"10" rSup { size 8{ - 2} } } {} Mass of a hummingbird 10 − 8 size 12{"10" rSup { size 8{ - 8} } } {} Time for one oscillation of an FM radio wave
10 − 6 size 12{"10" rSup { size 8{ - 6} } } {} Wavelength of visible light 1 size 12{"1"} {} Mass of a liter of water (about a quart) 10 − 3 size 12{"10" rSup { size 8{ - 3} } } {} Duration of a nerve impulse
10 − 3 size 12{"10" rSup { size 8{ - 3} } } {} Size of a grain of sand 10 2 size 12{"10" rSup { size 8{2} } } {} Mass of a person 1 size 12{"1"} {} Time for one heartbeat
1 size 12{"1"} {} Height of a 4-year-old child 10 3 size 12{"10" rSup { size 8{3} } } {} Mass of a car 10 5 size 12{"10" rSup { size 8{5} } } {} One day 8 . 64 × 10 4 s size 12{8 "." "64" times "10" rSup { size 8{4} } `s} {}
10 2 size 12{"10" rSup { size 8{2} } } {} Length of a football field 10 8 size 12{"10" rSup { size 8{8} } } {} Mass of a large ship 10 7 size 12{"10" rSup { size 8{7} } } {} One year (y) 3 . 16 × 10 7 s size 12{3 "." "16" times "10" rSup { size 8{7} } `s} {}
10 4 size 12{"10" rSup { size 8{4} } } {} Greatest ocean depth 10 12 size 12{"10" rSup { size 8{"12"} } } {} Mass of a large iceberg 10 9 size 12{"10" rSup { size 8{9} } } {} About half the life expectancy of a human
10 7 size 12{"10" rSup { size 8{7} } } {} Diameter of the Earth 10 15 size 12{"10" rSup { size 8{"15"} } } {} Mass of the nucleus of a comet 10 11 size 12{"10" rSup { size 8{"11"} } } {} Recorded history
10 11 size 12{"10" rSup { size 8{"11"} } } {} Distance from the Earth to the Sun 10 23 size 12{"10" rSup { size 8{"23"} } } {} Mass of the Moon 7 . 35 × 10 22  kg size 12{7 "." "35" times "10" rSup { size 8{"22"} } `"kg"} {} 10 17 size 12{"10" rSup { size 8{"17"} } } {} Age of the Earth
10 16 size 12{"10" rSup { size 8{"16"} } } {} Distance traveled by light in 1 year (a light year) 10 25 size 12{"10" rSup { size 8{"25"} } } {} Mass of the Earth 5 . 97 × 10 24  kg size 12{5 "." "97" times "10" rSup { size 8{"24"} } `"kg"} {} 10 18 size 12{"10" rSup { size 8{"18"} } } {} Age of the universe
10 21 size 12{"10" rSup { size 8{"21"} } } {} Diameter of the Milky Way galaxy 10 30 size 12{"10" rSup { size 8{"30"} } } {} Mass of the Sun 1 . 99 × 10 30  kg size 12{1 "." "99" times "10" rSup { size 8{"30"} } `"kg"} {}
10 22 size 12{"10" rSup { size 8{"22"} } } {} Distance from the Earth to the nearest large galaxy (Andromeda) 10 42 size 12{"10" rSup { size 8{"42"} } } {} Mass of the Milky Way galaxy (current upper limit)
10 26 size 12{"10" rSup { size 8{"26"} } } {} Distance from the Earth to the edges of the known universe 10 53 size 12{"10" rSup { size 8{"53"} } } {} Mass of the known universe (current upper limit)

Unit conversions: a short drive home

Suppose that you drive the 10.0 km from your university to home in 20.0 min. Calculate your average speed (a) in kilometers per hour (km/h) and (b) in meters per second (m/s). (Note: Average speed is distance traveled divided by time of travel.)

Strategy

First we calculate the average speed using the given units. Then we can get the average speed into the desired units by picking the correct conversion factor and multiplying by it. The correct conversion factor is the one that cancels the unwanted unit and leaves the desired unit in its place.

Solution for (a)

(1) Calculate average speed. Average speed is distance traveled divided by time of travel. (Take this definition as a given for now—average speed and other motion concepts will be covered in a later module.) In equation form,

average speed = distance time . size 12{"average speed = " { {"distance"} over {"time"} } } {}

(2) Substitute the given values for distance and time.

average speed = 10 . 0  km 20 . 0  min = 0 . 500  km  min . size 12{"average speed = " { {"10" "." 0" km"} over {"20" "." 0" min"} } =0 "." "500" { {"km"} over {"min"} } } {}

(3) Convert km/min to km/h: multiply by the conversion factor that will cancel minutes and leave hours. That conversion factor is 60 min/hr size 12{"60 min/hr"}{} . Thus,

average speed = 0 . 500  km  min × 60  min 1  h = 30 . 0  km  h . size 12{"average speed = "0 "." "500" { {"km"} over {"min"} } times { {"60"" min"} over {1" h"} } ="30" "." 0 { {"km"} over {h} } } {}

Discussion for (a)

Questions & Answers

how did you get 1640
Noor Reply
If auger is pair are the roots of equation x2+5x-3=0
Peter Reply
Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.
MATTHEW Reply
420
Sharon
from theory: distance [miles] = speed [mph] × time [hours] info #1 speed_Dennis × 1.5 = speed_Wayne × 2 => speed_Wayne = 0.75 × speed_Dennis (i) info #2 speed_Dennis = speed_Wayne + 7 [mph] (ii) use (i) in (ii) => [...] speed_Dennis = 28 mph speed_Wayne = 21 mph
George
Let W be Wayne's speed in miles per hour and D be Dennis's speed in miles per hour. We know that W + 7 = D and W * 2 = D * 1.5. Substituting the first equation into the second: W * 2 = (W + 7) * 1.5 W * 2 = W * 1.5 + 7 * 1.5 0.5 * W = 7 * 1.5 W = 7 * 3 or 21 W is 21 D = W + 7 D = 21 + 7 D = 28
Salma
Devon is 32 32​​ years older than his son, Milan. The sum of both their ages is 54 54​. Using the variables d d​ and m m​ to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.
Aaron Reply
find product (-6m+6) ( 3m²+4m-3)
SIMRAN Reply
-42m²+60m-18
Salma
what is the solution
bill
how did you arrive at this answer?
bill
-24m+3+3mÁ^2
Susan
i really want to learn
Amira
I only got 42 the rest i don't know how to solve it. Please i need help from anyone to help me improve my solving mathematics please
Amira
Hw did u arrive to this answer.
Aphelele
hi
Bajemah
-6m(3mA²+4m-3)+6(3mA²+4m-3) =-18m²A²-24m²+18m+18mA²+24m-18 Rearrange like items -18m²A²-24m²+42m+18A²-18
Salma
complete the table of valuesfor each given equatio then graph. 1.x+2y=3
Jovelyn Reply
x=3-2y
Salma
y=x+3/2
Salma
Hi
Enock
given that (7x-5):(2+4x)=8:7find the value of x
Nandala
3x-12y=18
Kelvin
please why isn't that the 0is in ten thousand place
Grace Reply
please why is it that the 0is in the place of ten thousand
Grace
Send the example to me here and let me see
Stephen
A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of one of the other legs. Find the lengths of the hypotenuse and the other leg
Marry Reply
how far
Abubakar
cool u
Enock
state in which quadrant or on which axis each of the following angles given measure. in standard position would lie 89°
Abegail Reply
hello
BenJay
hi
Method
I am eliacin, I need your help in maths
Rood
how can I help
Sir
hmm can we speak here?
Amoon
however, may I ask you some questions about Algarba?
Amoon
hi
Enock
what the last part of the problem mean?
Roger
The Jones family took a 15 mile canoe ride down the Indian River in three hours. After lunch, the return trip back up the river took five hours. Find the rate, in mph, of the canoe in still water and the rate of the current.
cameron Reply
Shakir works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925.
mahnoor Reply
I'm guessing, but it's somewhere around $4335.00 I think
Lewis
12% of sales will need to exceed 925 - 500, or 425 to exceed fixed amount option. What amount of sales does that equal? 425 ÷ (12÷100) = 3541.67. So the answer is sales greater than 3541.67. Check: Sales = 3542 Commission 12%=425.04 Pay = 500 + 425.04 = 925.04. 925.04 > 925.00
Munster
difference between rational and irrational numbers
Arundhati Reply
When traveling to Great Britain, Bethany exchanged $602 US dollars into £515 British pounds. How many pounds did she receive for each US dollar?
Jakoiya Reply
how to reduced echelon form
Solomon Reply
Jazmine trained for 3 hours on Saturday. She ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. What is her running speed?
Zack Reply
d=r×t the equation would be 8/r+24/r+4=3 worked out
Sheirtina
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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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