



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
An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
lim x to infinity e^1e^1/log(1+x)
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12, 17, 22.... 25th term
Akash
College algebra is really hard?
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
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hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
sure. what is your question?
ninjadapaul
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X6)^2
so it's 20 divided by X6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
is it a question of log
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
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How do i figure this problem out.
how do you translate this in Algebraic Expressions
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)1/7 (x1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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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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