



A commuter train travels from Baltimore to Washington, DC, and back in 1 hour and 45 minutes. The distance between the two stations is approximately 40 miles. What is (a) the average velocity of the train, and (b) the average speed of the train in m/s?
(a) The average velocity of the train is zero because
${x}_{\mathrm{f}}={x}_{0}$ ; the train ends up at the same place it starts.
(b) The average speed of the train is calculated below. Note that the train travels 40 miles one way and 40 miles back, for a total distance of 80 miles.
$\frac{\text{distance}}{\text{time}}=\frac{\text{80 miles}}{\text{105 minutes}}$
$\frac{\text{80 miles}}{\text{105 minutes}}\times \frac{\text{5280 feet}}{\text{1 mile}}\times \frac{\text{1 meter}}{3\text{.}\text{28 feet}}\times \frac{\text{1 minute}}{\text{60 seconds}}=\text{20 m/s}$
Section summary
 Time is measured in terms of change, and its SI unit is the second (s). Elapsed time for an event is
$\mathrm{\Delta}t={t}_{\mathrm{f}}{t}_{0},$
where
${t}_{\mathrm{f}}$ is the final time and
${t}_{0}$ is the initial time. The initial time is often taken to be zero, as if measured with a stopwatch; the elapsed time is then just
$t$ .
 Average velocity
$\stackrel{}{v}$ is defined as displacement divided by the travel time. In symbols, average velocity is
$\stackrel{}{v}=\frac{\mathrm{\Delta}x}{\mathrm{\Delta}t}=\frac{{x}_{\text{f}}{x}_{0}}{{t}_{\text{f}}{t}_{0}}\text{.}$
 The SI unit for velocity is m/s.
 Velocity is a vector and thus has a direction.
 Instantaneous velocity
$v$ is the velocity at a specific instant or the average velocity for an infinitesimal interval.
 Instantaneous speed is the magnitude of the instantaneous velocity.
 Instantaneous speed is a scalar quantity, as it has no direction specified.
 Average speed is the total distance traveled divided by the elapsed time. (Average speed is
not the magnitude of the average velocity.) Speed is a scalar quantity; it has no direction associated with it.
Conceptual questions
Give an example (but not one from the text) of a device used to measure time and identify what change in that device indicates a change in time.
There is a distinction between average speed and the magnitude of average velocity. Give an example that illustrates the difference between these two quantities.
Does a car's odometer measure position or displacement? Does its speedometer measure speed or velocity?
If you divide the total distance traveled on a car trip (as determined by the odometer) by the time for the trip, are you calculating the average speed or the magnitude of the average velocity? Under what circumstances are these two quantities the same?
How are instantaneous velocity and instantaneous speed related to one another? How do they differ?
Problems&Exercises
(a) Calculate Earth's average speed relative to the Sun. (b) What is its average velocity over a period of one year?
(a)
$3\text{.}\text{0}\times {\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}\text{m/s}$
(b) 0 m/s
A helicopter blade spins at exactly 100 revolutions per minute. Its tip is 5.00 m from the center of rotation. (a) Calculate the average speed of the blade tip in the helicopter's frame of reference. (b) What is its average velocity over one revolution?
The North American and European continents are moving apart at a rate of about 3 cm/y. At this rate how long will it take them to drift 500 km farther apart than they are at present?
$2\times {\text{10}}^{7}\phantom{\rule{0.25em}{0ex}}\text{years}$
Land west of the San Andreas fault in southern California is moving at an average velocity of about 6 cm/y northwest relative to land east of the fault. Los Angeles is west of the fault and may thus someday be at the same latitude as San Francisco, which is east of the fault. How far in the future will this occur if the displacement to be made is 590 km northwest, assuming the motion remains constant?
Questions & Answers
Introduction about quantum dots in nanotechnology
nano basically means 10^(9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials and their applications of sensors.
what is system testing?
AMJAD
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:
OpenStax, Sample chapters: openstax college physics for ap® courses. OpenStax CNX. Oct 23, 2015 Download for free at http://legacy.cnx.org/content/col11896/1.9
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