Barbara Perez

Assignment

Lecture 3/14/07

Kinematics

For each of the following questions, decide whether the question is asking for the distance or the magnitude of the displacement. Describe your reasoning.

  1. How far do you walk each day?

This question is asking for distance because the path that you walk matters.

  1. How far is it from Toronto to Mexico City by airplane?

This question is asking for magnitude of displacement if it is a one-way trip because the path that is flown doesn’t matter and they don’t count the miles that you ascend to get to cruising altitude or descend upon landing. If you’re talking about round trip, then I would still say magnitude of displacement but, you need to measure each segment separately.

  1. How far is it from Toronto to Mexico City by car?

This question is asking for distance because the path that is driven matters.

  1. How far is the earth from the moon?

This question is asking for magnitude of displacement because the path is not important.

  1. How long is a standard sheet of plywood?

I think in this case distance because there is no direction.

  1. How long is the coastline of Britain?

This question is asking distance because you break the coastline down into segments and measure the path of each one. The total distance you get depends on the length of the segments you break it up into.

  1. How long is the Nile?

This question is asking for magnitude of displacement because you don’t normally measure every curve of the river, but just from the beginning to the end which is magnitude of displacement.

  1. How long is the track on a compact disc?

This question is asking for distance because it is circular and from beginning to end is 360 degrees and you will end up where you started. If you used magnitude of displacement, it would be zero.

  1. How long did it take you to get here?

This question is asking for distance because the path you took to get here will have an impact on the length of time that it took you to get here.

  1. How many frequent flyer miles do you have?

This question is asking for magnitude of displacement because the airline usually has a standard distance for each flight and do not go by the route that is taken.

  1. What is the radius of the earth?

I think in this case is magnitude of displacement because there is a direction.

Use the following conversion factors:

1 mi = 5280 ft 1 ft = 12 in 1 in = 2.54 cm 1 m = 100 cm 1 km = 1000 m

1 h = 60 min 1 min = 60 s

to convert 60 mi/h (mph) to km/h (kph), to ft/s, and to m/s.

60 mi/h x 5280 ft/mi = 316,800 ft/h

316,800 ft/h x 12 in/ft = 3,801,600 in/h

3,801,600 in/h x 2.54 cm = 9,656,064 cm/h

9,656,064 cm/h x 1 m/100 cm = 96,560.64 m/h

96,560.64 m/h x 1 km/1000 m = 96.56064 km/h

60 mi/h x 5280 ft/mi = 316,800 ft/h

316,800 ft/h x 1 h/60 min = 5,280 ft/min

5,280 ft/min x 1 min/60 sec = 88 ft/s

60 mi/h x 5280 ft/mi = 316,800 ft/h

316,800 ft/h x 12 in/ft = 3,801,600 in/h

3,801,600 in/h x 2.54 cm = 9,656,064 cm/h

9,656,064 cm/h x 1 m/100 cm = 96,560.64 m/h

96,560.64 m/h x 1 h/60 min = 1,609.344 m/min

1,609.344 m/min x 1 min/60 sec = 26.8224 m/s

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 13.5cm/s swim for an equivalent distance of 94km without a rest. For how long was the larva swimming?

94 km x 1000 m/1 km = 94,000 m

94,000 m x 100 cm/1 m = 9,400,000 cm

9,400,000 cm/13.5cm/s = 696,296.2963 s

696296.2963 s/60 s/min = 11,604.93827 min

11,604.93827 min/60 min/h = 193.4656378 h

193.4656378 h/ 24h/day = 8.061068242 days

8 days, 1 hour, 27 minutes, 56 seconds

Another distance functions s(t) that will provide a good illustration.