Video Transcript
Two aircraft fly along the paths
shown, each flying for the same amount of time. Which color arrow shows the path of
the aircraft that flies between its initial and final positions at the greater
velocity? (A) The blue arrow, (B) the green
arrow, (C) the velocities are the same.
Comparing these two aircraft, we
see they each travel between an initial and a final position that are separated by
the same amount of vertical and horizontal distance. We want to know which one travels
between the initial and final positions at the greater velocity. Let’s remember a general equation
for velocity. It’s equal to an object’s
displacement divided by the time taken to be displaced some amount. The fact that we’re considering
displacement is key.
Displacement, we recall, only takes
into consideration the start and endpoints of an object’s motion. So the displacement of the plane
following the green arrow is given by this arrow, and the displacement of the plane
following the blue arrows is given by this arrow. These displacements are the
same. And since the planes both flew for
the same amount of time between their initial and final positions, we can say that
since each plane had the same displacement and the same amount of time elapsed, the
velocities of both aircraft are the same. As a side note, the speeds of these
aircraft are not the same. But since velocity depends on
displacement and both planes have the same displacement, their velocities are indeed
equal.
