What are some examples of displacement?

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Mr K Share
May 20, 2014

There are two different meanings for displacement: first it is the distance and direction from the starting place; second it can be the volume displaced when an object sinks or floats (see Archimedes principle).

I'm assuming that you are asking about the first definition. Displacement is the distance and direction from the starting point. If the motion is one dimension (forward and back or up and down) then displacement is equal to the distance. For example a runner running a 100 meter race on a straightaway has run a distance of 100 meters at the finish line. Her displacement is 100 meters forward. Second example: a rocket that goes 500 meters straight up has traveled a distance of 500 meters. Its displacement is 500 meters up.

However, direction matters. If the runner the the example above runs 400 meters around a track, coming back to the same point, the distance run is 400 meters, but the displacement is zero.

If the rocket in the second example falls 300 meters after reaching its peak, the distance it has traveled is 800 meters (500 up and 300 down). Its displacement is 200 meters up.

In two dimensions you need to use trigonometry to find the displacement. A boat that moves 3 km east and then 4 km North has a displacement of 5 km at an angle of 53 degrees north of east. Use the pythagorean theorem (it's a 3,4,5 triangle) and get the angle by using the inverse tangent function.

Displacement can be funny sometimes. If you return to the place of your birth, your displacement for your entire life is zero! (Have you never gone anywhere?!)

Finally, a question for you: does the odometer on your car tell you the cars distance or displacement? Hint: does it say zero if you drive back home?

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EET-AP Share
Nov 10, 2017

Answer:

To give examples of displacement, we must first define the term, and see where the definition takes us! Displacement occurs when an object is moved from dis-place to dat-place in a recorded direction.

Explanation:

Suppose we borrowed one of those huge helicopters and hooked it up to the Eiffel Tower to carry it away to Vienna, Austria. This is an example of displacement of a large icon along the 48th parallel of latitude over a distance of 1,033.81 km due east.

Or, we could mimic this displacement by moving a candle-stick from one side of a 1.03m table to the other side of the table, as long as we do it in the east direction.

Then we have a jogger who runs #60m# east, when he discovers he dropped his phone, and turns back west 45m where he sees the phone. Turning back again to continue his easterly run he covers another #60m#. His total displacement is #75m# east, although he has run a distance of #60m+45m+60m=195m#.

Image by EET-AP

There is displacement around a curve. When the earth completes a rotation in one day it also travels in its orbit around the sun #1/(365 1/4)# of the length of its orbit, or about #1/(365 1/4)xx940 million km#.

There is negative displacement:
https://socratic.org/questions/can-displacement-be-negative

And zero displacement takes place for every object that returns to its original location. Like the Eiffel Tower. We'll return it!
Displacement will always be less than the distance moved, except in the case of straight line motion in a particular direction.

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