Distance And Displacement An Activity
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Distance and Displacement
Distance : I've got to assume that everybody reading this has an idea of what distance is. It's one of those innate concepts that doesn't seem to require explanation. Nevertheless I've come up with a preliminary definition that I think is rather good. Distance is a measure of the interval between two locations. (This is not the final definition.) The "distance" is the answer to the question, "How far is it from this to that or between this and that?"
how far is itpossible answerstandard answer
earth to sun1 astronomical unit1.496 × 1011 m
66th to 86th Street in NYC1 mile1.609 × 103 m
heel to toe on a man's foot1 foot3.048 × 10−1 m
You get the idea. The odd thing is that sometimes we state distances as times.
how far is itpossible answerstandard answer
space shuttle orbitninety minutes per orbit40,000,000 m
Chicago to Milwaukeeninety minutes by car150,000 m
Central Park to Battery Parkninety minutes on foot10,000 m
They're all ninety minutes, but nobody but a fool would say they were they were all the same distance. What's being described in these examples is not distance, but time. In casual conversation, it's often all right to state distances this way, but in most of physics this is unacceptable.
Displacement :That being said, let me deconstruct the definition of distance I just gave you. Every year in class, I do the same moronic demonstration where I start at one side of the lecture table and walk to the other side and then ask "How far have I gone?"
There are two ways to answer this question. On the one hand, there's the sum of the smaller motions that I made: two meters east, two meters south, two meters west; resulting in a total walk of six meters. On the other hand, the end point of my walk is two meters to the south of my starting point. So which answer is correct? Well, both. The question is ambiguous and depends on whether the questioner meant to ask for the distance or displacement.
Let's clarify by defining each of these words more precisely. Distance is a scalar measure of the interval between two locations measured along the actual path connecting them. Displacement is a vector measure of the interval between two locations measured along the shortest path connecting them.
How far does the earth travel in one year? In terms of distance, quite far (the circumference of the earth's orbit is nearly one trillion meters), but in terms of displacement, not far at all (zero, actually). At the end of a year's time the earth is right.
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