Video Transcript
Which of the uniformly moving
objects shown have the greatest speed relative to each other?
The question is asking which two
objects’ speeds have the greatest difference between them. A good way to think about this
question is to imagine yourself in a car going at the speed of one of the objects,
let’s say, object A. If you see a car travelling at the
speed of object B, will it be passing you or will you be passing it? How quickly? And how about a car travelling at
the speed of object C? Repeat this thought experiment but
imagine your car is traveling at object B’s speed. Which car would pass you, object A
or C or none?
In this way, you can answer this
question. For a more mathematical approach,
we can turn to our trusty motion diagram. We like to represent shapes and
objects as dots to reduce confusion over object location. So we can represent the original
image like this. In this diagram, each dot
represents the object’s location at a certain time. Each dot is a snapshot of the
object’s location at one time unit, let’s say, one second after the last, and is
labeled with the second the snapshot was taken.
Recall now the equation for
speed. Since the time elapsed is always
one second, we can just pay attention to the distance traveled by each object. That will tell us all we need to
know about each object’s speed at a given moment. Notice too that the distance that
each object travels between snapshots is the same. So each object has uniform speed
throughout its journey. And this does make this question a
little easier to solve.
Now we’ve seen the motion diagram,
let’s think about the speed of each object. Object B travels the greatest
distance between seconds, whilst object A travels the least distance, and object C
travels the median or middle amount of distance each second. This can be represented in a
similar way as shown.
Now that we know which object moves
at what speed, we need to compare the speeds to each other. In this image, we represent the
differences in two objects’ speed at a time. The relative speeds of objects A
and C and B and C are almost the same, though objects B and C have a slightly slower
relative speed, but the relative speed of objects A and B is much greater. Thus, we found the answer to our
question. Objects A and B have the greatest
relative speed, or greatest difference in speed.
