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.
