The Physics
Opus in profectus

Speed & Velocity

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  1. Calculate the size of a light year.
  2. How fast is a point on the equator moving due to the rotation of the Earth?
  3. 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…
    1. speed
    2. velocity
    … for the entire journey.
  4. A problem for residents of the US only. Convert 60 mph (highway speed) to…
    1. km/h
    2. m/s


  1. In an unusual move by the New York State Department of Transportation, all of the "speed limit" signs were replaced with "velocity limit" signs.
    1. What would such a sign look like?
    2. How could one travel faster than the old speed limit without violating the new velocity limit?
  2. Which device(s) on a car can be used to change…
    1. its speed?
    2. its velocity but not its speed?
  3. A car driving on a circular test track shows a constant speedometer reading of 100 kph for one lap.
    1. Describe the car's speed during this time.
    2. Describe its velocity.
    3. How do the speed and velocity compare?
  4. Is it possible for an object to have…
    1. constant speed and changing velocity
    2. changing speed and constant velocity
  5. Consider the following hypothetical quantity of motion — the rate of change of time with distance traveled.
    1. Under what circumstances would this new quantity…
      1. have a large value?
      2. have a small value?
      3. equal zero?
      Use real objects doing real actions as examples whenever possible.
    2. Invent an appropriate name for this new quantity. (There is no single metaphysical "right answer", but there are an infinite number of wrong answers.)
  6. Why are the devices in cars called speedometers and not velocitometers?


  1. The World Snail Racing Championships have been held in the English village of Congham, Norfolk since the 1960s. (Despite the international title, "foreign snails are not allowed.") The contestants are placed at the center of a circular table covered with a damp tablecloth and race outwards 13 inches (33 cm) towards the finish line. A contestant known only as Archie set the current world record of 2 minutes 20 seconds in 1995. Determine Archie's speed in…
    1. m/s
    2. km/h
  2. 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?
  3. 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?
  4. A high speed video camera running at 180 frames per second was used to record a player kicking a soccer ball (Source: 所さんの目がテン!). Each square on the grid behind the ball is 10 cm on a side.
    1. View the video and then determine the speed of the soccer ball.
    2. Penalty kicks in soccer take place 11.0 m away from the goal. Calculate the time it takes the ball to cover this distance.

    Slow motion video of a soccer player kicking a soccerball in front of a 10 cm grid.

  5. 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?
  6. 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?
  7. 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?
  8. 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.
    1. If a cheetah were to run at top speed for 3.0 s, how far would it travel?
    2. How long would it take the sloth to "run" this same distance?
  9. Calculate the orbital speed of the moon.
  10. Calculate the orbital speed of the Earth.
  11. A common measure of astronomical distances is the light year. This is the distance a beam of light would travel in a vacuum in one year (about 10 trillion kilometers). As an exercise calculate the size of a…
    1. light  day
    2. light hour
    3. light minute
    4. light second
    5. light millisecond
    6. light microsecond
    7. light nanosecond
    8. light picosecond
    9. light femtosecond
  12. 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 signal to travel from the Earth to the object and back?
    1. Earth's moon
    2. the sun
    3. Mars (when closest to the Earth)
    4. Pluto (when farthest from the Earth)
  13. At one time, the great goal of middle distance runners was the four minute mile.
    1. What is the average speed of a runner capable of this feat in mph and m/s?
    2. How long would it take to complete a marathon (26 miles 385 yards) at this pace?
  14. Isaac Newton was born in Woolsthorpe Manor, Lincolnshire on 25 December 1642 and died in Kensington, London on 20 March 1727.
    1. Determine the displacement from Woolsthorpe Manor to Kensigton.
    2. Determine the span of Mr. Newton's life.
    3. Calculate the average velocity of Mr. Newton over his lifetime in m/s.
    4. Why is it appropriate to ask for the average velocity and not the instantaneous velocity?
    5. Why is it appropriate to ask for the average velocity and not the average speed?
    6. If Mr. Newton had instead lived until 25 June 1811, what total displacement would he have experienced over his lifetime? Where would he have died?
  15. 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…
    1. 20 m
    2. 10 m
    3. 5 m
    4. 1 m
  16. 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.
  17. 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 to an exotic distant location
    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 ? ? ?


  1. track-events.txt
    This file gives the world record times for eight track events.
    1. Calculate the speed of each runner.
    2. Determine…
      1. the effect of gender on speed.
      2. the effect of distance on speed.
    1. Event (length in meters)
    2. Men's record times (seconds)
    3. Women's record times (seconds)
    Source: International Association of Athletics Federations (20 August 2010).


  1. 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, Voyage  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 magnitude of the following quantities in m/s relative to the sun…
    Voyager Project
    quantity voyager 1 voyager 2
    speed, instantaneous    
    speed, average    
    velocity, instantaneous    
    velocity, average    
  2. 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 Wikipedia's List of physicists.
  3. 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…
    1. from the hub to the primary destination
    2. from the primary destination to the secondary destination
    3. from the hub to the secondary destination
  4. 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…
    1. the first taxi ride
    2. the plane flight
    3. the second taxi ride
    4. the entire trip
  5. 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…
    1. walking at a casual pace?
    2. running at marathon speed?
    3. driving at freeway speed?
    4. flying in a commercial airplane?
    5. riding a rifle bullet?
    6. riding a beam of light?