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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?
(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?
On May 26, 1934, a streamlined, stainless steel diesel train called the Zephyr set the world’s nonstop long-distance speed record for trains. Its run from Denver to Chicago took 13 hours, 4 minutes, 58 seconds, and was witnessed by more than a million people along the route. The total distance traveled was 1633.8 km. What was its average speed in km/h and m/s?
$\text{34}\text{.}\text{689 m/s}=\text{124}\text{.}\text{88 km/h}$
Tidal friction is slowing the rotation of the Earth. As a result, the orbit of the Moon is increasing in radius at a rate of approximately 4 cm/year. Assuming this to be a constant rate, how many years will pass before the radius of the Moon’s orbit increases by $3\text{.}\text{84}\times {\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\mathrm{m}$ (1%)?
A student drove to the university from her home and noted that the odometer reading of her car increased by 12.0 km. The trip took 18.0 min. (a) What was her average speed? (b) If the straight-line distance from her home to the university is 10.3 km in a direction $\text{25}\text{.}\mathrm{0\xba}$ south of east, what was her average velocity? (c) If she returned home by the same path 7 h 30 min after she left, what were her average speed and velocity for the entire trip?
(a) $\text{40}\text{.}\text{0 km/h}$
(b) 34.3 km/h, $\text{25\xba}\phantom{\rule{0.25em}{0ex}}\text{S of E}\text{.}$
(c) $\text{average speed}=\text{3.20 km/h,}\phantom{\rule{0.25em}{0ex}}\stackrel{-}{v}=0.$
The speed of propagation of the action potential (an electrical signal) in a nerve cell depends (inversely) on the diameter of the axon (nerve fiber). If the nerve cell connecting the spinal cord to your feet is 1.1 m long, and the nerve impulse speed is 18 m/s, how long does it take for the nerve signal to travel this distance?
Conversations with astronauts on the lunar surface were characterized by a kind of echo in which the earthbound person’s voice was so loud in the astronaut’s space helmet that it was picked up by the astronaut’s microphone and transmitted back to Earth. It is reasonable to assume that the echo time equals the time necessary for the radio wave to travel from the Earth to the Moon and back (that is, neglecting any time delays in the electronic equipment). Calculate the distance from Earth to the Moon given that the echo time was 2.56 s and that radio waves travel at the speed of light $(3\text{.}\text{00}\times {\text{10}}^{8}\phantom{\rule{0.25em}{0ex}}\text{m/s})$ .
384,000 km
A football quarterback runs 15.0 m straight down the playing field in 2.50 s. He is then hit and pushed 3.00 m straight backward in 1.75 s. He breaks the tackle and runs straight forward another 21.0 m in 5.20 s. Calculate his average velocity (a) for each of the three intervals and (b) for the entire motion.
The planetary model of the atom pictures electrons orbiting the atomic nucleus much as planets orbit the Sun. In this model you can view hydrogen, the simplest atom, as having a single electron in a circular orbit $1\text{.}\text{06}\times {\text{10}}^{-\text{10}}\phantom{\rule{0.25em}{0ex}}\text{m}$ in diameter. (a) If the average speed of the electron in this orbit is known to be $2\text{.}\text{20}\times {\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\text{m/s}$ , calculate the number of revolutions per second it makes about the nucleus. (b) What is the electron’s average velocity?
(a) $6\text{.}\text{61}\times {\text{10}}^{\text{15}}\phantom{\rule{0.25em}{0ex}}\text{rev/s}$
(b) 0 m/s
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