Video Transcript
Which of the uniformly moving
objects shown have the least speed relative to each other? (A) Object A and Object B, (B)
Object A and Object C, or (C) Object B and Object C.
This question is asking which two
objects have the least speed relative to each other. We can understand what relative
speed means by imagining being in a moving car driving on a straight road where cars
can travel in the same direction on two lanes that are side by side.
Imagine that you turn to look out
the side window of your car and see another car alongside your car. The other car is traveling in the
same direction as your car. If your car and the other car are
traveling at the same speed, the cars will stay alongside each other. The relative speed between your car
and the other car will be zero, because there is no difference between their
speeds. If your car is traveling at a
greater speed than the other car, your car will start to pull ahead. In this case, there will be some
relative speed between your car and the other car, because there is a difference in
the speeds at which they are traveling.
If your car is traveling at a
lesser speed than the other car, that car will start to pull ahead. In this case, there will again be
some relative speed between your car and the other car. This is because there is a
difference in the speeds at which they are traveling.
Let us see how this idea of
relative motion relates to the question. We see that each object is shown at
four different positions. For all three objects, the
distances between each position they are shown and the position below or above that
position are the same.
Recall that the question states
that the objects are all moving uniformly, meaning moving at constant speeds. The objects having constant speeds
and equal changes in position means that the positions of the objects shown must be
their positions at the start and end of a time interval. The time interval must be the same
for all the objects because each object is shown in four positions. The speed of an object is equal to
the distance it’s traveled divided by the time it’s taken to travel this
distance. This means that if each object is
shown at the start and end of the same time interval, the objects that have traveled
a greater distance must have a greater speed.
All of the objects are traveling in
the same direction. We can now think of the objects as
being like side-by-side cars. All the objects start alongside
each other. If we compare Object A to Object B,
we can see that Object B is pulling ahead of Object A. Object B has a greater speed than
Object A. If we compare Object B to Object C,
we can see that Object B is pulling ahead of Object C. Object B has a greater speed than
Object C. If we compare Object A to Object C,
we can see that Object C is pulling ahead of Object A. Object C has a greater speed than
Object A. So, from all of this, we can see
that Object B has the greatest speed of all the objects and Object A has the least
speed of all the objects.
However, the question wants us to
work out which two objects have the least speed relative to each other. This is really just the same as
asking which two objects have the least difference in speed from each other. We can do this by comparing the
distance that each object has traveled. We can immediately see that each
object has traveled a different distance, so they must have different speeds.
We know that Object B has the
greatest speed and Object A has the least speed. Therefore, Object B and Object A
have the greatest difference in speed. As these two objects have the
greatest difference in speed, we can rule out the corresponding answer option,
option (A).
The objects that have the least
difference is speed must then either be Object B and Object C or Object A and Object
C. These correspond to answer option
(B) and answer option (C). What we must determine is if the
difference between the speed of Object B and Object C is a greater difference than
the difference between the speed of Object A and Object C.
Recall that the objects that have
traveled a greater distance must have traveled a greater speed. Therefore, the objects with a
greater difference in distance traveled must have a greater difference in speed. We can see that the difference in
distance traveled by Object B and Object C is smaller than the difference in
distance traveled by Object A and Object C. Therefore, Object B and Object C
have a smaller difference in speed than Object A and Object C. So, we can rule out answer option
(B), Object A and Object C. And we can accept answer option
(C), Object B and Object C, as our correct answer.
The uniformly moving objects shown
that have the least speed relative to each other are Object B and Object C.
