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?
We’re told here that these grid
spaces each have a side length of one meter and that the arrows show the distances
moved by the orange and blue objects in each second of time. Knowing this, we want to solve for
the speed of either of these objects relative to the other. To get started, let’s recall the
mathematical expression for relative speed. The speed of one object relative to
another is the change in distance between them divided by the change in time.
For our blue and orange objects,
we’ll say that they had their original positions at a time of zero seconds. Then each object moved for one
second to reach its final position. The total change in time, then, is
just one second. That’s the time period over which
both objects were moving. Over that time, we see the orange
object moved one, two, three grid spaces; that’s three meters. Meanwhile, the blue object moved
one, two grid spaces or two meters. The change in distance between
these two moving objects is three meters plus two meters. We get a result of five meters per
second.
Note that because these objects are
approaching one another, their relative speed is how many meters closer one object
gets to the other object per second. If instead they have been moving
away from one another, their relative speed is how many meters away one object gets
from the other in each second of time. So, five meters per second is the
speed of the orange object relative to the blue object. And it’s also the speed of the blue
object relative to the orange object. That is, it’s the speed of either
object relative to the other.
