Video Transcript
The positions of two objects are
shown at one-second time intervals, starting at a time of zero seconds. Between what times is the average
speed of object A greater than the average speed of object B? (A) Zero seconds and one second,
(B) one second and two seconds, (C) two seconds and three seconds, or (D) zero
seconds and three seconds.
Here, we have two moving triangular
objects and multiple snapshots of their positions, sort of like a time-lapse
photo. The snapshots are all taken one
second apart, and we can count four different snapshots. We’ve been told that the first
snapshot, which is at the very bottom, was taken at a time of zero seconds. After this, there are three more,
so we’re able to see where the objects are at a time of one, two, and three seconds
after the initial snapshot. Therefore, this diagram shows the
changing positions of the objects over a total time interval of three seconds.
Notice that both objects are moving
in the same direction, but they’re not moving at the same speed as each other. If the objects did move at the same
speed as each other, we would see them perfectly side by side in every snapshot. But this is not the case.
Now, this question is asking us to
compare their speeds and identify a time interval during which object A moves faster
on average than object B. Looking at the diagram, we can see
that over the complete three-second time interval, object B covers more total
distance than object A. Recall that the speed of an object
measures the distance it moves divided by the time it takes. So, because object B moved farther
over the three seconds than object A did, object B has a greater average speed over
that time interval. Answer choice (D) says the opposite
thing. It suggests that object A has a
greater average speed between zero and three seconds. We know that this is not
correct. So let’s eliminate this option.
Notice that the other answer
choices are talking about smaller time intervals, each one second long. To think about these intermediate
time intervals, it would be helpful to label the diagram to show the time at which
each snapshot was taken. Also, to help simplify the diagram,
let’s imagine that the objects leave behind marks at regular time intervals. And we can represent the marks left
by the objects as dots to clearly show their positions at different times.
Now, let’s take a closer look at
the objects’ motion. For object A, we can see that
there’s an equal distance between each snapshot. This means that it covers the same
distance over each one-second interval. So we know that object A travels at
a uniform or constant speed. Object B, however, travels at a
nonconstant speed because we can see that over each one-second interval, it travels
a different distance. Because object B changes speed, we
can only say what average speed it has in each time interval. Between zero and one second, object
B doesn’t move very far, so it has a low average speed. Over the next second though, we see
a much bigger distance traveled, so it has a relatively high average speed. Then, between two and three
seconds, it moves a different kind of moderate distance. So here, it’s moving faster than it
was in its first second of motion, but slower than it was moving in the next
second.
Now, it’s our job to compare these
different speeds to the constant unchanging speed of object A. Answer choice (A) refers to the
very first second of motion and suggests that object A had a faster average speed
than object B during this interval. This agrees with our diagram. We can see that object A actually
did move farther than object B did in the very first second. So option (A) seems like the
correct answer.
Still though, let’s take a look at
options (B) and (C) just to be sure. Answer choice (B) suggests that
object A has a higher average speed than object B between one and two seconds. Looking at the diagram, we can see
that object B actually moves away farther than object A does during this
interval. This means that object B had the
greater average speed then. So let’s eliminate this answer
choice. Moving on, option (C) refers to the
final second of motion. Comparing the distances traveled by
the two objects over this interval, we can see that object B moves farther in that
one second than object A does. And therefore, object B has a
greater average speed. Answer choice (C) is wrong as
well.
This gives us even more confidence
in answer choice (A). During the first second of motion,
object A travels a farther distance than object B. This means that over the time
interval between zero seconds and one second, object A has a greater average speed
than object B.
