Question Video: Calculating the Relative Speed of Two Moving Objects Science

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.