practice
- Calculate the size of a light year.
- How fast is a point on the equator moving due to the rotation of the earth?
- I went for a walk one day. I walked north 6.0 km at 6.0 km/h and then west 10 km at 5.0 km/hr. Determine the average speed for the entire journey.
- A problem for residents of the US only. Convert 60 mph (highway speed) to …
- km/h
- m/s
conceptual
- In an unusual move by the New York State Department of Transportation, all of
the "speed limit" signs were replaced with "velocity limit" signs.
- What would such a sign look like?
- How could one travel faster than the old speed limit without violating the new velocity limit?
- Which device(s) on a car can be used to change …
- its speed?
- its velocity but not its speed?
- A car driving on a circular test track shows a constant speedometer reading of
100 kph for one lap.
- Describe the car's speed during this time.
- Describe its velocity.
- How do the speed and velocity compare?
- Is it possible for an object to have …
- constant speed and changing velocity,
- changing speed and constant velocity?
- Speed is the rate of change of distance with time. Consider a new, as yet, undefined
quantity -- the inverse ratio, the rate of change of time with distance.
- Under what circumstances would this new quantity
- have a large value?
- have a small value?
- equal zero?
- Invent an appropriate name for this new quantity.
- Why are the devices in cars called speedometers and not velocitometers?
numerical
- The fastest speed achieved by a snail in the Guinness Gastropod Championship,
held over a 330 mm (13 in) course in the O'Conor Don pub in central
London is held by a mollusk called Archie, which took 2 minutes and 20 seconds
to cover the course. Determine Archie's speed in m/s and km/h.
- A moving driver not anticipating an accident can apply the brakes fully in about
0.5 s. How far would a car driving down the freeway at 30 m/s travel
in this time?
- In an experiment at James Cook University in Australia, a researcher put the
larvae of tropical fish in a special tank to measure their swimming speeds. The
tank generates an adjustable current that the fish must swim against. The most
proficient swimmer was a surgeonfish larva that maintained a 13.5 cm/s swim
for an equivalent distance of 94 km without a rest. For how long was the
larva swimming?
- A high speed video camera running at 180
frames per second was used to record a player kicking a soccer ball. Each square
on the grid behind the ball is 10 cm on a side.
- View the video and then determine the speed of the soccer ball. The video
is available in .gif or .mov formats.
- Penalty kicks in soccer take place 11.0 m away from the goal. Calculate
the time it takes the ball to cover this distance.
- When designing aircraft it is common to place them in a wind tunnel: a closed
room where air is blown at high speed. As an option, some tests can be performed
in an indoor hyperballistic range. In one such range, aircraft models are projected
at 9000 m/s (20,000 mph) into a catching device designed to recover them
intact. Ultra-high-speed cameras with laser illumination then photograph the
model at exposures of 20 ns. How far will such a model move while it is
being photographed?
- It takes a plane flying at 150 km/h 3.0 minutes to circle a cloud at
an altitude of 3,000 m. What is the diameter of the cloud?
- The three-toed sloth is the slowest land mammal. On the ground, the sloth moves
at an average speed of 0.23 m/s (0.5 mph). The cheetah is the fastest
land mammal. A cheetah is capable of speeds up to 31 m/s (70 mph) for
brief periods. If a cheetah were to run at top speed for 3.0 s, how long
would it take the sloth to catch up?
- Calculate the orbital speed of the moon.
- Calculate the orbital speed of the earth.
- Calculate the size of a …
- light-day
- light-hour
- light-minute
- light-second
- light-millisecond
- light-microsecond
- light-nanosecond
- light-picosecond
- light-femtosecond
- Radio waves travel at the speed of light. Calculate the "round trip light
time" for the following astronomical objects. That is, how long would it take a radio
signal to travel from the earth to the object and back?
- earth's moon
- the sun
- Mars (when closest to the earth)
- Pluto (when farthest from the earth)
- At one time, the great goal of middle distance runners was the four minute mile.
- What is the average speed of a runner capable of this feat in mph and m/s?
- How long would it take to complete a marathon (26 miles 385 yards)
at this pace?
- Isaac Newton was born in Lincolnshire, near Grantham, on 25 December 1642, and died
in Kensington, London, on 20 March 1727.
Grantham is approximately 160 km north of London.
- Calculate the average velocity of Mr. Newton over his lifetime in m/s.
- Why does this problem ask for the average velocity and not the instantaneous velocity?
- Why does this problem ask for the average velocity and not the average speed?
- If Mr. Newton had instead lived until 13 June 1811,
what total displacement would he have experienced over his lifetime? Where would he have died?
- A stunt crew is planning a chase scene for a movie. The script calls for a car
to drive across a railroad track moments before a train enters the crossing.
(Warning: Don't try this at home!) The locomotive engineer recommends a speed
of 10 m/s for safety and the director wants the car moving at 30 m/s
for excitement. Where should the rear of the car be when the train is at the
following distances from the crossing …
- 20 m,
- 10 m,
- 5 m,
and
- 1 m?
- The same crew members from the previous problem, now have to prepare another
stunt for the same movie. They plan to have a second car drive off a ramp at
the train. The jump will be timed so that an empty flatcar will roll into the
crossing and the pursuing car will then be able to slip through the gap and continue
the chase. (Warning: Don't try this at home! If you do, you are seriously stupid.)
The flatcar is 16 m long by 3 m wide and that the pursuing car is 4 m
long by 2 m wide. The train is still moving at 10 m/s. Determine the
minimum speed at which the car must be driven off the ramp.
- Here are some data for a three segment trip to an exotic distant location. Calculate
the missing data and complete the table below.
| A Three Segment Trip |
| trip segment |
distance traveled |
elapsed time |
average speed |
| by plane |
6930 km |
? |
965 km/h |
| by taxi |
201 km |
2.90 h |
? |
| on foot |
? |
5.75 h |
4.50 km/h |
| entire trip |
? |
? |
? |
statistical
- hawaiian-chain.txt
The Hawaiian Island chain is more than just the visible islands. It also includes
a few dozen seamounts -- islands that have eroded down below sea level. The combined
Hawaiian Islands--Emperor Seamounts chain is a series of volcanic structures
formed by a single, long-lived plume of magma referred to as a "hotspot".
The hotspot stayed fixed as the pacific plate slowly moved over it, resulting
in a chain of volcanoes stretching from the Aleutian Islands off the coast of
Alaska to Mount Kilauea on the Big Island of Hawaii in the tropics. Use the data
set in the accompanying text file to determine the speed of the Pacific plate
in cm/yr.
The columns in this data set are as follows:
- volcano number
- volcano name
- volcano age (millions of years)
- distance from Kilauea (km)
- error in age (millions of years)
- error in distance (km)
- track-events.txt
This file gives the world record times for eight track events as of August 1999.
Calculate the average speed of each record holder. From these numbers determine …
- the effect of gender on speed
- the effect of distance on speed
in track events at the elite level.
The columns in this data set are as follows:
- event distance (m)
- men's record time, hours portion
- men's record time, minutes portion
- men's record time, seconds portion
- women's record time, hours portion
- women's record time, minutes portion
- women's record time, seconds portion
investigative
- Repeat the last statistical problem above, but this time …
- use the world records in swimming,
- use the results from a local track and field competition,
- use the results from a local swimming competition, or
- use the results from several different years to determine the trend in the speed of women compared to the speed of men. Predict the year when they will equal.
- The twin spacecraft Voyager 1 and Voyager 2 were launched by NASA in the summer
of 1977 from Cape Canaveral, Florida. As originally designed, the Voyagers were
to conduct close up studies of Jupiter and Saturn. Eventually, Voyager 2 would
go on to explore Uranus and Neptune. The spacecraft are still operating and continue
to return data about interplanetary space. Range,
velocity, and round trip light time for the Voyagers are available at the
Voyager Project web
site. Using the data at this site, determine the following quantities in m/s …
- the instantaneous and average speed of each spacecraft,
- the magnitude of the instantaneous and average velocity of each spacecraft, and
- the speed of light.
- Obtain the necessary biographical information needed to determine the magnitude
of the average velocity of a dead physicist over his or her lifetime in m/s.
For a list of physicist with online biographies see
Yahoo! Science: Physics: Physicists.
- Obtain an airline timetable for the planes departing from a hub airport. Find
a flight that continues on to a second destination after a brief layover. Use
the data to calculate the average speed of this plane …
- from the hub to the primary destination,
- from the primary destination to the secondary destination, and
- from the hub to the secondary destination.
- Obtain the door-to-door travel info from your home to the center of another city
on a nonstop flight. Include the duration of the two taxi rides, arrival and
departure times for the plane, distance of each taxi ride, distance of the plane
flight, recommended check in time, and an estimate of the time it takes to exit
the plane, gather up your luggage, and hail a taxi. Calculate the average speed
of …
- the first taxi ride,
- the plane flight,
- the second taxi ride, and
- the entire trip.
- Assuming it were possible, how long would it take to travel from the earth to
Mars along a straight line on the day of their closest approach by …
- walking at a casual pace?
- running at marathon speeds?
- driving at freeways speeds?
- flying in a commercial airplane?
- riding a rifle bullet?
- riding a beam of light?
