Video Transcript
The car shown is at the center of a
circle. The car moves a distance of 30
meters. What could its final position
be? (A) Any point within the
circle. (B) Only points on the
circumference of the circle.
This question asks us, if the car
moves a distance of 30 meters from its starting point at the center of the circle,
where will it end up? The key to this question is to
notice the use of the word distance, not displacement.
Remember that distance is a measure
of how far an object travels in total, whereas displacement only considers the
distance from an object’s starting point to its ending point in a particular
direction. So, if the car moves in something
other than a straight line, the distance and the displacement will not be the
same.
To understand this difference,
consider this image. If an object travels from point 𝐴
to point 𝐶, stopping at point 𝐵 first, then it travels a distance that is equal to
the length of this path. But the object’s displacement is
equal to the length of the straight line segment from 𝐴 to 𝐶. Here, we can see that the distance
traveled by the object is greater than its displacement. If, however, the object moved from
𝐴 straight to 𝐶, without changing direction, then the distance it traveled would
be equal to its displacement.
Let’s go back to the car. Although the car travels 30 meters,
the distance between the car’s starting point and ending point does not have to be
30 meters. If the displacement was 30 meters,
then the car would have to end up at some point on the circle’s circumference. This is because all points on a
circle are exactly one radius length away from the center. The radius of this circle is 30
meters. Since the car begins at the center,
any point on the circle would be a 30-meter displacement. On the other hand, to travel a
total distance of 30 meters, the car does not have to travel in just one
direction.
Remember that distance is a scalar
quantity and has no direction. Instead, the driver could choose to
travel back and forth one meter 15 times or drive three times in a circle of a
circumference 10 meters. Either way, the distance covered
would be 30 meters.
So, we have two possible
scenarios. If the car moved in a straight line
in one direction, its displacement as well as its total distance is equal to 30
meters. And the car can end up at any point
on the circumference of the circle, as described in option (B). If the car drives in any number of
directions for a total distance of 30 meters, the car can end up at any point inside
the circumference of the circle. So, the car can either be on the
circumference of the circle or any point inside the circumference. This corresponds to answer option
(A): the car can be at any point within the circle. So, option (A) is the correct
answer.
