Video Transcript
The speed of a toy car is measured
by recording its position each second. Between which of the following
times is the average speed of the car the greatest? (A) From when measuring starts to
one second after measuring starts. (B) From one second after measuring
starts to two seconds after measuring starts. (C) From two seconds after
measuring starts to three seconds after measuring starts.
We’ve been given a diagram here
showing a toy car that’s moving to the right. Specifically, we’re shown the
position of the car at four different times as it moves. The car begins its journey over
here at the very instant we start the measurement. Then, one second later, we can see
that the car has moved to the right. After one more second has passed,
the car has moved further to the right. And then we can also see the car’s
position after yet one more second has passed at the final moment of
measurement. Here, a total of three seconds have
passed.
As the car moves, we can roughly
track how far it goes using these one-meter markings up above. Remember that the car moves over
three one-second intervals. From the diagram, we can see that
the car moves a different distance over each one-second interval. We can recall that if an object
does not travel equal distances in equal intervals of times, then it does not move
at a constant speed. Rather, we say that the car moves
with variable speed. This means that the car moves at
different speeds at different times. And this question is simply asking
us when did the car move the fastest.
To answer this, we need to compare
the speed of the car during each of the one-second intervals. Let’s recall that the average speed
of an object over a given amount of time is equal to the distance traveled divided
by the time over which that distance is traveled. In this case, all of the time
intervals are one second long. So, to compare the car’s speed
during those time intervals, we only need to look at the distance the car traveled
in each interval. The car must have traveled at the
greatest average speed during the one-second interval when it traveled the greatest
distance.
So, the question is, during which
time interval did the car travel the greatest distance? Looking at the diagram, we see that
the car traveled the greatest distance between one second after measuring starts and
two seconds after measuring starts. In the first interval, the car
travels one meter. In the second interval, the car
travels a distance greater than one meter. In the third interval, the car
travels less than one meter. So we see that this second
interval, between one and two seconds after measuring starts, is the only one in
which the distance traveled is greater than one meter. Since the car travels the greatest
distance in this interval, then we know that the car had the greatest average speed
in this interval between one and two seconds after measuring starts.
Our answer then is option (B). The car has the greatest average
speed from one second after measuring starts to two seconds after measuring
starts.
