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Vectors

Vectors

Figure 1

An object moves from point A to point B along the curved path shown ( Figure 1 ).

Supposing that we are not interested in the actual path followed but only in the result: that the object was displaced from A to B. How do we represent this Displacement?


Figure 2

We represent it by a straight arrow as shown in Figure 2. What information does the arrow give us? The length of the arrow is proportional to the distance between the end points and it points in the direction of the displacement.

The displacement of an object is an example of a vector.


Figure 3

The displacement of an object depends only on its starting point and its end point, it does not depend on the path taken. The two curved paths shown on the left correspond to the same displacement vector.

If I start someplace, go right around our galaxy and come back to the starting point, the displacement is zero. It is a vector of length zero.

Q. What is the relation between the displacement and the distance traveled?

A. There is really no relation. The most you can say is that the distance is greater than or equal to the magnitude of the displacement.

The magnitude of the displacement is not the distance.

Displacement is a vector. We represent vectors by arrows.

How do we describe vectors? We describe a vector by its magnitude (length) and its direction (the angle it makes with a given direction, say, North).

When a particle moved along a line (motion in 1-D), positive displacement meant that it ended up at a point to the right of the starting point, negative displacement meant that it ended up to the left of the starting point. The sign gave us the direction, the magnitude the amount.

Q. An object is displaced by 30 m east. Where is it now located?

A. The displacement does not tell us the particle's position unless we know where it started from. Suppose one object underwent a displacement of 30 m east starting at some point in Madras and another one, starting at some point in Mumbai. Both displacements are identical, but their positions are different.

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