Video Transcript
The positions of two objects are
shown at one-second time intervals. Which object has the greater
difference between its greatest average speed over one second and its least average
speed over one second? Is it (A) object A, (B) object B,
or (C) the difference between the greatest average speed over one second and the
least average speed over one second is the same for both objects?
Recall that speed is the distance
traveled in a time interval. The time intervals for which each
of the objects in this question travel are all equal to one second. And because the time intervals are
all equal, this question can be answered by simply observing the distance each
object travels in each time interval.
One way to help understand what the
diagram shows is to imagine that the objects are moving along the ground and we are
looking down at the objects from above. As such, we can imagine that the
back of each object makes a mark on the ground at regular time intervals. If we do this, we can imagine the
marks left on the ground as shown. In this motion diagram, we see the
distance each object moves in one-second time intervals.
Next, we know that speed can be
represented by the equation speed is equal to distance traveled divided by time
traveled for. Since we’re only looking at equal
one-second time intervals for both objects, we can ignore the variable of time used
in the equation. As such, we only need to compare
the distance each object travels in each time interval to compare the average speed
of the objects in the time interval .
It is clear from the diagram that
object A travels the same distance in each time interval. Therefore, we can say that object A
moves uniformly, meaning it moves at a constant speed. As the time interval between each
dot is one second and the distance between each dot and the nearest dot to it is
equal for all the dots, object A never moves a greater or lesser distance in one
second than in the second before or the second after.
Object B, on the other hand, does
not travel the same distance in each time interval. And as such, the speed of object B
is not the same in each time interval. Because object B changes speed, we
can only say what average speed it has in each time interval.
The question asked us “Which object
has the greater difference between its greatest and least average speed?” As the speed of object A is
constant, the average speed does not change. And so the difference between the
greatest and least average speed of object A must be zero. However, as the average speed of
object B is not the same in all the time intervals, there is a difference between
the greatest and least average speed of object B that must be greater than zero. We can therefore conclude that the
answer must be (B). Object B has the greatest
difference in average speed over one second.
