Video Transcript
A blue object and an orange object
move across a grid of lines spaced one meter apart. The arrows show the distances that
the objects move in each second. What is the speed of either object
relative to the other?
To find the relative speed between
these objects, let’s start by recalling the mathematical equation for relative
speed. For two objects, the relative speed
between them equals the change in distance between them divided by the change in
time. So, for our orange and blue
objects, we’ll first figure out how the distance between them changes. And then, we’ll see over what
interval of time that change occurs.
We see that the initial position of
the orange object is here and the initial position of the blue object is here. That is, at first, these objects
are separated by one, two, three, four grid spaces. Each grid space is one meter of
distance, so four grid spaces is four meters. Both of these objects then move and
so that they reach final positions at these locations. At the end of this time interval,
the orange and blue objects are one, two, three grid spaces apart. The change in distance between them
then is the larger distance minus the smaller one. All this change occurred over some
time interval.
We’re told that in our diagram the
arrows show the distances that the objects move in each second of time. Since there’s one arrow for each
object, we know that each object moved for one second. The total change in time then is
just the one second over which both the orange and blue objects were in motion. Four meters minus three meters is
one meter. So, the relative speed between
these objects is one meter per second.
Note that to calculate this
relative speed, we needed to subtract one distance from another. This happens whenever our two
objects are moving in the same direction. If they had been moving apart, we
could have approached the problem differently. All that said, the speed of the
orange object relative to the blue and the blue relative to the orange is one meter
per second.
