Video Transcript
A car is at the center of a
circle. The arrows show paths that the car
could travel to reach the circumference of the circle. Is the distance moved the same for
both paths? Is it (A) yes or (B) no?
This question asks us whether the
red and blue arrows cover the same distance from start to finish. Recall the definition of distance:
a scalar quantity whose magnitude is the length of the path the object travels from
start to finish. Distance does not take into
consideration the object’s direction along the path. And unlike displacement, distance
is not necessarily the shortest path the object takes. An object may travel in zigzags or
curves to get from its start to finish. Distance takes all of this travel
into consideration, whereas displacement does not.
In this case, however, we are
looking at straight-line motion. Both the red and blue arrows are
perfectly straight. They overlap perfectly too, meaning
they are pointing along the same direction. This fact is useful to know because
of the definition of the circle. To get from the center of a circle
to any point on its circumference, an object must travel along a path whose length
is equal to the length of the radius of the circle. Since both arrows originate at the
center and end at the same point on the circumference of the circle, we can say that
they are both the length of the circle’s radius.
The two arrows have the same length
or magnitude. So we can therefore say the
distance the car moves is the same if it were to follow either the red or the blue
path. The correct answer is option (A),
yes.
