Video Transcript
An aircraft follows the curved line
shown. Which has greater magnitude, the
aircraft’s speed or its velocity? (A) Velocity, (B) speed.
In this question, we must work out
whether the aircraft shown in the diagram has a greater speed or velocity. We can recall that the speed of an
object is equal to the distance it travels divided by the time it takes to travel
this distance. Speed is a scalar quantity, so it
only has magnitude.
This is different to velocity. Velocity is a vector quantity and
therefore has both direction and magnitude. The magnitude of the velocity of an
object is equal to the magnitude of the displacement between the object’s starting
and ending positions divided by the time taken to travel between those
positions.
So, in order to answer this
question, we must look at the distance the aircraft has traveled and compare it to
the displacement between its starting and ending positions.
Let’s now recall that the magnitude
of the displacement between two points is equal to the straight-line distance
between them. We can add displacement to our
diagram by drawing a straight arrow between the aircraft’s initial position and
final position. We can also remember that a
straight line is the shortest path between two points. Because the aircraft follows a
curved path, we can see that the distance it travels must be greater than the
magnitude of its displacement. And because distance is greater
than the magnitude of the displacement, we know that the speed of the aircraft must
be greater than the magnitude of its velocity.
So, the aircraft’s speed has a
greater magnitude than its velocity. The correct answer is option (B),
speed.
