A blue object and an orange object
move across a grid of lines spaced one meter apart. Each object moves for two
seconds. The arrows show the distances that
the objects move in each second. What is the relative speed at which
the objects approach each other?
In this question, we are asked to
find the speed of either of the objects shown relative to each other. From the question, we know that
each object moves for two seconds and each grid line is spaced one meter apart.
Now, looking at the arrows in the
diagram, we can see that the objects are traveling in opposite directions and each
object travels two meters during the two seconds. First, we can determine the speed
of each object. Recall that speed is equal to the
distance traveled divided by the time traveled for. In this question, each object
travels two meters in two seconds. So each object has the speed of one
meter per second.
Let’s take a closer look at the
changes in the distance between these objects. Each time that the blue object
travels one meter closer to the orange object, the orange object also travels one
meter but in the opposite direction to the blue object. Therefore, we can see that the
distance between the objects is changing as the objects move.
We can then define an equation for
relative speed, recalling that relative speed equals the change in distance divided
by the time.
Now, let’s take a look at the
distance each object travels so we can find the change in distance between them. Each object travels two meters
towards the other. So let’s add these distances to
find the total change in distance of the objects as they approach each other. When we add these distances, we get
a total change in the distance between our objects of four meters. And this change happens in the two
seconds for which the objects travel.
We can use these values of distance
and time in the equation for relative speed to find the relative speed at which the
objects approach each other. Relative speed is equal to the
change in distance divided by the time traveled for. In this question, relative speed is
equal to four meters divided by two seconds. Simplifying this, we can see that
the objects are approaching each other at a speed of two meters per second. This is the relative speed of the
objects as they move.