A blue object moves across a grid
of lines spaced one meter apart. The object moves for two
seconds. The arrows show the distance that
the object moves in each second. What is the speed of the object
relative to the grid lines that it crosses?
Looking at these grid spaces, we’re
told that the side of each square has a length of one meter. We’re also told that the arrows —
there’s one here and one here — show the distance that the object moves over each
second of time. In the first second, the object
moves one grid space. That’s one meter of distance. In the second second, it also moves
one meter. We want to find the speed of this
object relative to the grid lines. To do this, let’s recall that the
relative speed between two objects equals the change in distance between them
divided by the change in time.
In this scenario, our blue object
is definitely in motion, while our grid lines are not; they don’t move at all. So, the only change in distance
between our objects will be caused by the motion of our blue object. The amount of time over which the
blue object is in motion is one second plus one second. And we saw that in each of those
seconds the blue object moves one grid space or one meter. Therefore, the blue object has
moved two meters in two seconds. Its speed then is one meter per
second. This is the speed of the blue
object relative to the grid lines. And notice since the grid lines
aren’t moving at all, it’s also the absolute speed of the blue object.
Whenever we have two objects where
one object is moving and one is not, the relative speed between them is the same as
the moving object’s absolute speed.