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To check your answer, consider the following:

(1) Be sure that you have properly cancelled the units in the unit conversion. If you have written the unit conversion factor upside down, the units will not cancel properly in the equation. If you accidentally get the ratio upside down, then the units will not cancel; rather, they will give you the wrong units as follows:

 km min × 1  hr 60  min = 1 60  km hr  min 2 , size 12{ { {"km"} over {"min"} } times { {1`"hr"} over {"60"`"min"} } = { {1} over {"60"} } { {"km" cdot "hr"} over {"min"} } } {}

which are obviously not the desired units of km/h.

(2) Check that the units of the final answer are the desired units. The problem asked us to solve for average speed in units of km/h and we have indeed obtained these units.

(3) Check the significant figures. Because each of the values given in the problem has three significant figures, the answer should also have three significant figures. The answer 30.0 km/hr does indeed have three significant figures, so this is appropriate. Note that the significant figures in the conversion factor are not relevant because an hour is defined to be 60 minutes, so the precision of the conversion factor is perfect.

(4) Next, check whether the answer is reasonable. Let us consider some information from the problem—if you travel 10 km in a third of an hour (20 min), you would travel three times that far in an hour. The answer does seem reasonable.

Solution for (b)

There are several ways to convert the average speed into meters per second.

(1) Start with the answer to (a) and convert km/h to m/s. Two conversion factors are needed—one to convert hours to seconds, and another to convert kilometers to meters.

(2) Multiplying by these yields

Average speed = 30 . 0 km h × 1 h 3,600 s × 1, 000 m 1 km , size 12{"Average"`"speed"="30" "." 0 { {"km"} over {h} } times { {1" h"} over {"3,600 s"} } times { {1,"000"" m"} over {"1 km"} } } {}
Average speed = 8 . 33 m s . size 12{"Average"`"speed"=8 "." "33" { {m} over {s} } } {}

Discussion for (b)

If we had started with 0.500 km/min, we would have needed different conversion factors, but the answer would have been the same: 8.33 m/s.

You may have noted that the answers in the worked example just covered were given to three digits. Why? When do you need to be concerned about the number of digits in something you calculate? Why not write down all the digits your calculator produces? The module Accuracy, Precision, and Significant Figures will help you answer these questions.

Nonstandard units

While there are numerous types of units that we are all familiar with, there are others that are much more obscure. For example, a firkin is a unit of volume that was once used to measure beer. One firkin equals about 34 liters. To learn more about nonstandard units, use a dictionary or encyclopedia to research different “weights and measures.” Take note of any unusual units, such as a barleycorn, that are not listed in the text. Think about how the unit is defined and state its relationship to SI units.

Some hummingbirds beat their wings more than 50 times per second. A scientist is measuring the time it takes for a hummingbird to beat its wings once. Which fundamental unit should the scientist use to describe the measurement? Which factor of 10 is the scientist likely to use to describe the motion precisely? Identify the metric prefix that corresponds to this factor of 10.

The scientist will measure the time between each movement using the fundamental unit of seconds. Because the wings beat so fast, the scientist will probably need to measure in milliseconds, or 10 3 size 12{"10" rSup { size 8{ - 3} } } {} seconds. (50 beats per second corresponds to 20 milliseconds per beat.)

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One cubic centimeter is equal to one milliliter. What does this tell you about the different units in the SI metric system?

The fundamental unit of length (meter) is probably used to create the derived unit of volume (liter). The measure of a milliliter is dependent on the measure of a centimeter.

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Summary

  • Physical quantities are a characteristic or property of an object that can be measured or calculated from other measurements.
  • Units are standards for expressing and comparing the measurement of physical quantities. All units can be expressed as combinations of four fundamental units.
  • The four fundamental units we will use in this text are the meter (for length), the kilogram (for mass), the second (for time), and the ampere (for electric current). These units are part of the metric system, which uses powers of 10 to relate quantities over the vast ranges encountered in nature.
  • The four fundamental units are abbreviated as follows: meter, m; kilogram, kg; second, s; and ampere, A. The metric system also uses a standard set of prefixes to denote each order of magnitude greater than or lesser than the fundamental unit itself.
  • Unit conversions involve changing a value expressed in one type of unit to another type of unit. This is done by using conversion factors, which are ratios relating equal quantities of different units.

Conceptual questions

Identify some advantages of metric units.

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Problems&Exercises

The speed limit on some interstate highways is roughly 100 km/h. (a) What is this in meters per second? (b) How many miles per hour is this?

  1. 27 . 8 m/s size 12{"27" "." 8`"m/s"} {}
  2. 62 . 1 mph size 12{"62" "." 1" mph"} {}
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A car is traveling at a speed of 33 m/s size 12{"33"" m/s"} {} . (a) What is its speed in kilometers per hour? (b) Is it exceeding the 90 km/h size 12{"90"" km/h"} {} speed limit?

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Show that 1 . 0 m/s = 3 . 6 km/h size 12{1 "." 0`"m/s"=3 "." "6 km/h"} {} . Hint: Show the explicit steps involved in converting 1 . 0 m/s = 3 . 6 km/h. size 12{1 "." 0`"m/s"=3 "." "6 km/h"} {}

1.0 m s = 1 . 0 m s × 3600 s 1 hr × 1 km 1000 m size 12{ { {1 "." "0 m"} over {s} } = { {1 "." "0 m"} over {s} } times { {"3600 s"} over {"hr"} } times { {1`"km"} over {"1000 m"} } } {}

= 3 . 6 km/h size 12{ {}=3 "." 6" km/h"} {} .

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American football is played on a 100-yd-long field, excluding the end zones. How long is the field in meters? (Assume that 1 meter equals 3.281 feet.)

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Soccer fields vary in size. A large soccer field is 115 m long and 85 m wide. What are its dimensions in feet and inches? (Assume that 1 meter equals 3.281 feet.)

length: 377 ft size 12{"377"" ft"} {} ; 4 . 53 × 10 3  in . size 12{4 "." "53" times "10" rSup { size 8{3} } " in" "." } {} width: 280 ft size 12{"280"" ft"} {} ; 3 . 3 × 10 3  in size 12{3 "." 3 times "10" rSup { size 8{3} } " in"} {} .

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What is the height in meters of a person who is 6 ft 1.0 in. tall? (Assume that 1 meter equals 39.37 in.)

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Mount Everest, at 29,028 feet, is the tallest mountain on the Earth. What is its height in kilometers? (Assume that 1 kilometer equals 3,281 feet.)

8 . 847 km size 12{8 "." "847"" km"} {}

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The speed of sound is measured to be 342 m/s size 12{"342"" m/s"} {} on a certain day. What is this in km/h?

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Tectonic plates are large segments of the Earth’s crust that move slowly. Suppose that one such plate has an average speed of 4.0 cm/year. (a) What distance does it move in 1 s at this speed? (b) What is its speed in kilometers per million years?

(a) 1 . 3 × 10 9  m size 12{1 "." 3 times "10" rSup { size 8{ - 9} } " m"} {}

(b) 40 km/My size 12{"40"" km/My"} {}

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(a) Refer to [link] to determine the average distance between the Earth and the Sun. Then calculate the average speed of the Earth in its orbit in kilometers per second. (b) What is this in meters per second?

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Questions & Answers

A soccer player kicked off a ball at velocity of 62 ft/s at angle 45°. A goal keeper is 43 yard away from the direction in which ball kicked off. At what minimum velocity he runs to meet the ball?
Ram Reply
A soccer player kicked off the ball at the velocity of 62 ft/s at 45° with horizontal.A goal keeper is 43 yard away from the ball kicked position.At what minimum velocity he runs to meet the ball?
Ram
what is torque
Deepak Reply
The turning effect of force is called torque.
Uzair
What is the effect of static electricity
Ruth
what there factors affect the surface tension of a liquid
Promise Reply
formula for impedance
muyiwa Reply
ehat is central forces
Nita Reply
what is distance?
Jonathan Reply
What does mean ohms law imply
Victoria Reply
ohms law state that the electricity passing through a metallic conductor is directly proportional to the potential difference across its end
muyiwa
what is matter
folajin Reply
Anything that occupies space
Kevin
Any thing that has weight and occupies space
Victoria
Anything which we can feel by any of our 5 sense organs
Suraj
Right
Roben
thanks
Suraj
what is a sulphate
Alo
any answers
Alo
the time rate of increase in velocity is called
Blessing Reply
acceleration
Emma
What is uniform velocity
Victoria
Greetings,users of that wonderful app.
Frank Reply
how to solve pressure?
Cruz Reply
how do we calculate weight and eara eg an elefant that weight 2000kg has four fits or legs search of surface eara is 0.1m2(1metre square) incontact with the ground=10m2(g =10m2)
Cruz
P=F/A
Mira
can someone derive the formula a little bit deeper?
Bern
what is coplanar force?
OLADITI Reply
forces acting and lying on d same plane
Promise
what is accuracy and precision
Peace Reply
How does a current follow?
Vineeta Reply
follow?
akif
which one dc or ac current.
akif
how does a current following?
Vineeta
?
akif
AC current
Vineeta
AC current follows due to changing electric field and magnetic field.
akif
you guys are just saying follow is flow not follow please
Abubakar
ok bro thanks
akif
flows
Abubakar
but i wanted to understand him/her in his own language
akif
but I think the statement is written in English not any other language
Abubakar
my mean that in which form he/she written this,will understand better in this form, i write.
akif
ok
Abubakar
ok thanks bro. my mistake
Vineeta
u are welcome
Abubakar
what is a semiconductor
Vineeta Reply
substances having lower forbidden gap between valence band and conduction band
akif
what is a conductor?
Vineeta
replace lower by higher only
akif
convert 56°c to kelvin
Abubakar
How does a current follow?
Vineeta
A semiconductor is any material whose conduction lies between that of a conductor and an insulator.
AKOWUAH

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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