Video Transcript
Which of the uniformly moving objects shown have the least speed relative to each
other?
The question asks, “Which two objects have the least speed relative to each
other?” Recall that the relative speed of two objects is the change in the distance between
those objects divided by the time that the objects move for. Now the objects in this question are stated to be moving uniformly. We can see that each object is shown at four different positions. And for each object, the distances between any two positions that are next to each
other are the same. This tells us that the objects all travel for the same amount of time. And so we’re seeing the positions of each of the objects at the start and end of
equal time intervals.
The length of each time interval isn’t stated in the question, so we can consider
them to have any value. A value of one second is convenient to choose. So if we choose a value of one second for the time intervals, we can show the
positions of the objects at the start and end of each time interval.
Because speed is equal to the distance traveled divided by the time traveled for and
because the objects will move for the same amount of time, we can answer this
question quite easily by just determining which two objects increase the distance
between each other the least in the time they travel for.
It is important to be clear that the distance between objects that we are considering
here is the distance along a line that they travel on. In the diagram, the objects all travel along vertical lines. So we’re only looking for the increase in the vertical distance between the
objects. Only the vertical positions of the objects need to be considered.
Let’s consider then the vertical positions of the objects at the end of the time that
they move for. For each object, we can draw an arrow showing where the start and end of the motion
of the object is. The vertical distance between two objects is the distance between the heads of the
arrows. The arrowheads show the positions of the objects at the end of the time that they
move for.
It’s important to notice that object C travels in the opposite direction to object A
and to object B. So let’s compare the distance traveled by object A and object B. We see that the arrow for object B is longer than the arrow for object A. So object B travels a greater distance than object A. We can in fact imagine object A and object B as cars traveling in the same direction
on a straight road. Object B travels further along the road than object A.
Recall also that object B travels in the opposite direction to object C. The further that object B travels in the opposite direction to object C, the more the
distance between object B and C increases. We can imagine object B and object C as cars traveling in opposite directions on a
straight road. We see then that the objects that increase the distance between each other the most
are object B and C. These are the objects that have the greatest speed relative to each other.
Object B and C cannot then have the least speed relative to each other. So either object A and object C have the least speed relative to each other, or
object A and object B have the least speed relative to each other. We must determine whether the distance between object A and B after the time that
they travel for is greater than or less than the distance between object A and C
after the time that they travel for.
Let’s compare these distances. We can use this comparison to see which is the lesser difference in distance. We can now see that the difference between the distances between objects A and
objects B after they’ve traveled is the lesser difference. So object A and object B have the least speed relative to each other.
