Physics A: Problem Set 4: Speed and velocity

classwork

1. A problem for residents of the US only. Convert 60 mph (a common highway speed) to…
   1. km/h
   2. m/s
2. At one time, the great goal of middle distance runners was the four minute mile. Determine the average speed of a runner capable of this feat in…
   1. mph
   2. m/s
3. 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?
4. 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 generated an adjustable current that the fish had to 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 champion larva swimming in this "fish treadmill"?

homework

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 9 km/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. 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
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.
   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?
8. 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.