Question Video: Understanding the Relation between Displacement and Distance | Nagwa Question Video: Understanding the Relation between Displacement and Distance | Nagwa

Question Video: Understanding the Relation between Displacement and Distance Science • Third Year of Preparatory School

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If a distance is traveled in a straight line, which of the following is correct? [A] The distance traveled is the magnitude of the displacement along the straight line. [B] The distance becomes a vector quantity.

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Video Transcript

If a distance is traveled in a straight line, which of the following is correct? Is it (A) the distance traveled is the magnitude of the displacement along the straight line? (B) The distance becomes a vector quantity.

This question asks us to describe a straight-line distance in terms of displacement. Recall the definition of a distance. The distance an object travels is the length of the path traveled between the start point and the endpoint of the motion of an object.

In this image, the object travels five meters. Five here is just a number we chose. We could have chosen any positive number. This definition of distance makes no mention of a direction. This is because distance is a scalar, not a vector, quantity. A scalar quantity has a magnitude but no direction. In this example, five meters is the magnitude of the distance traveled.

Unlike distance, displacement is a vector quantity. A vector quantity has both a magnitude and a direction. Let us recall the definition of displacement. The displacement of an object is the straight-line distance from one point to another point. The direction of a displacement is specified. It is the direction from a straight line from one point to another point. In this made-up example, the object travels five meters from left to right, so the direction of the displacement is to the right.

So if an object travels in a straight line, does this mean that the distance traveled becomes a vector quantity as option (B) states? No, it does not. Even if an object travels a certain distance and moves along a straight line throughout its travel, the distance does not tell us where the object moved from and where it moved to. If an object travels along a distance along a horizontal straight line, the object could have been traveling to the left or to the right. The distance traveled could have been in either direction. There is no way to know as distance does not specify a direction. We reject option (B).

Option (A) states that for an object that moves in a straight line, the distance traveled along the straight line is the magnitude of the displacement. We have said that a displacement is a straight-line distance from one point to another point. We can see from this that if an object travels from a point to another point in a straight line, then the magnitude of the displacement of the object equals the length of the straight line between the points. The length of the line is the magnitude of the distance traveled by the object. We can see that option (A) is correct, and so we accept option (A).

Strictly speaking, this isn’t always true. An object traveling along a line could reverse direction. If the object reversed direction, then it could travel along the length of the straight line in both directions. For an object that does not reverse direction though, it is the case that the magnitude of the displacement of the object equals the distance traveled by the object.

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